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Electromagnetic and Thermal Analysis of Microwave Heating in 915 MHz Single Mode Cavity Systems: Microwave Assisted Thermal Sterilization and Pasteurization

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ELECTROMAGNETIC AND THERMAL ANALYSIS OF MICROWAVE HEATING
IN 915 MHZ SINGLE MODE CAVITY SYSTEMS: MICROWAVE ASSISTED
THERMAL STERILIZATION AND PASTEURIZATION
By
DEEPALI JAIN
A dissertation submitted in partial fulfillment of
the requirements for the degree of
DOCTOR OF PHILOSOPHY
WASHINGTON STATE UNIVERSITY
Department of Biological Systems Engineering
DECEMBER 2017
ProQuest Number: 10639329
All rights reserved
INFORMATION TO ALL USERS
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a note will indicate the deletion.
ProQuest 10639329
Published by ProQuest LLC (2018 ). Copyright of the Dissertation is held by the Author.
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To the Faculty of Washington State University:
The members of the Committee appointed to examine the dissertation
of DEEPALI JAIN find it satisfactory and recommend that it be accepted.
Juming Tang, Ph.D., Chair
Patrick D. Pedrow, Ph.D.
Shyam Sablani, Ph.D.
ii
ACKNOWLEDGMENTS
My first and foremost gratitude goes to Professor Juming Tang for being my compass and
guide, as I embarked on a journey to do meaningful research in the field of food engineering. He is
the sole reason I have been able to write papers, be a part of exciting projects, attend conferences,
evolve into a better food engineer and have a great graduate school experience. He challenged me
with problems that pushed me to the edge, he corrected me whenever and wherever I went wrong,
and helped me connect the dots in my research. He kept me grounded, while encouraging my ideas
to fly above and beyond the normal realm, so that I could look at the big picture, while solving
practical problems for the food industry.
My committee members - Professors Patrick D. Pedrow and Shyam Sablani - selflessly contributed their time and advice to help me navigate interdisciplinary concepts I used in my research.
Their experience enriched my ideas, their wisdom helped me solve problems. Without their contributions, this dissertation would have never reached fruition.
I thank Stewart - our most amazing lab manager - who has also become a friend of mine in the
last five years. His management keeps the whole laboratory running and keeps everyones research
engines well greased. Huimin was just as resourceful and amazing in how she shaped my graduate
school and research experience. Every moment spent in the company of such extraordinary people
is worth its weight in gold. I must also thank Zhongwei, Frank Liu and Frank Younce for their
amazing patience throughout my lengthy working sessions and invaluable insights for my research
and papers.
iii
During these last five years - I made new friends and accomplices. I must give a huge shoutout to the members of the Food Engineering Club - both past, present, and future - for their dedication towards building a community of food engineers, and supporting each other in enhancing
interpersonal skills through a broad range of activities. I also thank them for their jokes that made
me laugh in dark hours, and their company and friendship in merry times. I could not have come
this far without them.
I spent a large amount of time in the laboratory, and thus, inevitably spending that time away
from home, family, and friends. I thank them for their understanding and sacrifices. I thank my
brother, Dr. Akshay Jain and his beautiful wife, Mahi, for the phone conversations and continuous encouragement from half-way across the world. I thank my sister, Garima, and my brilliant
brother-in-law, Mr. Ashish Jain - for supporting my dreams to come to USA to study food engineering and being an active part of the process from the beginning to end. Also, I thank my dearest
niece, Aashi, and sweetest nephew, Aarjav, for being the cutest children ever. They brought me
inexplicable joy and relief from anxiety in moments of crisis in their own ways - and I am sure I
couldn’t have done this without their love.
I thank Sayonsom - my dear husband, my best friend, and a companion like no other. For
serving the endless cocktails of humor and wisdom, that I binged on during the toughest phases of
writing this dissertation. I also thank him for inspiring me to believe that to do serious things in
life, we should not take ourselves too seriously.
And above all, my biggest gratitude goes to my mother, Abha Jain, and my father, Professor
Kamal C. Jain - who brought me to this world, nourished me, and helped me become the woman
that I am today. I endeavor every day to live my life by their endearing example - live by the same
principles, high values, and virtues that drive them. To them, I dedicate this dissertation.
iv
ELECTROMAGNETIC AND THERMAL ANALYSIS OF MICROWAVE HEATING
IN 915 MHZ SINGLE MODE CAVITY SYSTEMS: MICROWAVE ASSISTED
THERMAL STERILIZATION AND PASTEURIZATION
Abstract
by Deepali Jain, Ph.D.
Washington State University
December 2017
Chair: Juming Tang
Microwave assisted thermal sterilization and pasteurization (MATS and MAPS) systems have
great potential for the food industry to manufacture high quality and nutritious packaged foods
with clean labels. This dissertation aimed to develop tools which will aid in the commercialization
of the MATS and MAPS systems, and future development of food formulations and processing
schedules for efficient microwave processing. Chapter 1 provides an introduction, history and
fundamentals of food processing. Chapter 2 presents previous computer models and knowledge
gaps in microwave assisted thermal processing.
Chapter 3 describes faster browning of fructose under alkaline conditions as a time-temperature
indicator in microwave pasteurization processes. Reaction kinetics of browning showed a log linear relationship in the temperature range of 60-90°C. This non-enzymatic browning of fructose in
mashed potato model food provided an efficient, convenient and cost effective tool to determine
the heating patterns in MAPS system.
MAPS is a food processing technology which employs a novel way to transport food packages
inside the microwave cavity. Carriers made up of stainless steel and polyetherimide are used to
modify the electric field distribution and obtain uniform heating patterns. Chapter 4 presents a
v
computer simulation model and validation to analyze the effect of carriers on the electric field
inside the cavity. The effect of frequency fluctuations on heating pattern was also investigated
using computer simulations. The conclusion was reached that presence of metal food carriers
provided uniform, stable and predictable heating patterns.
In MAPS and MATS, 915 MHz microwaves are launched from top and bottom of the food
packages forming standing wave patterns within the foods. Chapter 5 discussed the development
of a 1-D analytical model to compare the heating rates of different foods processed in multicompartment and single compartment food packages. A novel dimensionless number (Jain-Tang)
is proposed and was validated to estimate the influence of food dielectric properties and food
thickness on microwave power dissipation. It was shown that this number can serve as a general
criteria to evaluate the effectiveness of microwave heating in packaged foods with pre-determined
dielectric properties and package thickness.
vi
TABLE OF CONTENTS
Page
ACKNOWLEDGMENTS ............................................................................................................. iii
ABSTRACT .....................................................................................................................................v
LIST OF TABLES ........................................................................................................................ xii
LIST OF FIGURES ..................................................................................................................... xiv
1. INTRODUCTION ......................................................................................................................1
1.1 Fundamentals of thermal processing ...................................................................................1
1.1.1 Sterilization .................................................................................................................2
1.1.2 Pasteurization .............................................................................................................2
1.2 Current needs of the food industry........................................................................................3
1.3 Recent developments in microwave processing of foods ....................................................4
1.4 Dissertation Objective ...........................................................................................................6
1.5 Dissertation Organization ....................................................................................................7
2. MODELING AND COMPUTER SIMULATIONS IN MICROWAVE ASSISTED
THERMAL PROCESSING .......................................................................................................8
2.1 Abstract .................................................................................................................................8
2.2 Introduction ..........................................................................................................................8
2.3 Maxwell’s equations coupled with heat transfer ..................................................................9
2.4 Numerical methods in microwave heating ........................................................................11
2.4.1 Finite Element method .............................................................................................12
2.4.2 Finite difference time domain ..................................................................................13
vii
2.5 Analytical solutions to Maxwell’s equations ...................................................................15
2.6 Simulation and modeling of microwave assisted thermal processing systems ................18
2.7 Validation techniques for MATS simulation models .........................................................24
2.7.1 Heating pattern validation ........................................................................................24
2.7.2 Temperature profile validation .................................................................................27
2.8 Knowledge gaps ..................................................................................................................28
3. APPLICATION OF NON-ENZYMATIC BROWNING OF FRUCTOSE FOR HEATING
PATTERN DETERMINATION IN MICROWAVE ASSISTED THERMAL
PASTEURIZATION SYSTEM ................................................................................................29
3.1 Abstract ..............................................................................................................................29
3.2 Introduction ........................................................................................................................30
3.3 Materials and Methods .......................................................................................................32
3.3.1 Food preparation and thermal treatment ..................................................................32
3.3.2 UV absorbance and browning ...................................................................................33
3.3.3 Modelling procedure ................................................................................................33
3.3.4 Food properties measurement ...................................................................................34
3.3.5 Microwave assisted thermal pasteurization (MAPS) processing .............................35
3.3.6 Heating pattern determination by computer vision assistant ....................................35
3.3.7 Temperature profile ..................................................................................................36
3.4 Results and Discussion .......................................................................................................38
3.4.1 Browning kinetics .....................................................................................................38
3.4.2 Color and lethality correlation .................................................................................41
3.4.3 Dielectric properties of model food ..........................................................................43
viii
3.4.4 Application of the mashed potato model food in MAPS processing .......................48
3.5 Conclusion ..........................................................................................................................52
4. EVALUATION OF FOOD CARRIER DESIGNS TO IMPROVE HEATING
UNIFORMITY IN MICROWAVE ASSISTED THERMAL PASTEURIZATION USING
COMPUTER SIMULATIONS ...............................................................................................53
4.1 Abstract ..............................................................................................................................53
4.2 Introduction ........................................................................................................................54
4.3 Materials and Methods .......................................................................................................55
4.3.1 Computer simulation procedure ...............................................................................55
4.3.2 Food carrier designs ..................................................................................................59
4.3.3 Electric field distribution and heating pattern analysis ...........................................65
4.3.4 Validation experiment procedure ............................................................................67
4.3.5 Effect of frequency on heating pattern ....................................................................68
4.4 Results and Discussion .......................................................................................................69
4.4.1 Dielectric and Thermal properties of food .......................................................69
4.4.2 Influence of food carriers on electromagnetic field distribution in MAPS ...69
4.4.3 Heating patterns using simulations and experiments .......................................73
4.4.4 Effect of frequency on heating pattern..............................................................76
4.5 Conclusion ..........................................................................................................................79
5. INFLUENCE OF DIELECTRIC PROPERTIES AND THICKNESS ON
ELECTROMAGNETIC HEATING OF FOODS IN 915 MHZ SINGLE MODE
MICROWAVE CAVITY .........................................................................................................80
ix
5.1 Abstract ..............................................................................................................................80
5.2 Introduction ........................................................................................................................81
5.3 Mathematical models .........................................................................................................84
5.3.1 Governing equations ..............................................................................................85
5.3.2 Electromagnetic power dissipation and heat transfer ..............................................87
5.4 Experimental validation .....................................................................................................89
5.4.1 Sample preparation ..................................................................................................89
5.4.2 Food properties measurement ..................................................................................90
5.4.3 Microwave assisted thermal sterilization (MATS) processing ................................90
5.5 Results and Discussion ......................................................................................................93
5.5.1 Analytical results ......................................................................................................93
5.5.2 Food properties and analytical temperature distribution in mashed potatoes,
peas and rice........................................................................................................... 103
5.5.3 Experimental results ...............................................................................................109
5.6 Conclusion .......................................................................................................................117
6. ANALYSIS OF TWO COMPARTMENT TRAYS HEATING PATTERNS IN
MICROWAVE
ASSISTED THERMAL PASTEURIZATION SYSTEM (MAPS) USING J-T NUMBER ...118
6.1 Abstract ............................................................................................................................118
6.2 Introduction ......................................................................................................................118
6.3 Materials and Methods ...................................................................................................120
x
6.3.1 Food preparation ....................................................................................................120
6.3.2 Food properties ......................................................................................................121
6.3.3 Microwave assisted thermal pasteurization (MAPS) processing............................123
6.3.4 Heating pattern determination by computer vision assistant .................................127
6.3.5 Temperature profile ................................................................................................127
6.4 Results and Discussion ....................................................................................................128
6.4.1 Food properties ......................................................................................................128
6.4.2 Heating pattern results ...........................................................................................128
6.4.3 Temperature profile ...............................................................................................133
6.5 Conclusion ..........................................................................................................................135
7. CONCLUSION & FUTURE WORK ......................................................................................136
7.1 Contributions of this dissertation .......................................................................................137
7.2 Future Works .....................................................................................................................138
APPENDIX
A. PLANE WAVE INCIDENCE FROM TOP AND BOTTOM OF A RECTANGULAR
DIELECTRIC SLAB .............................................................................................................140
B. ANALYSIS OF ELECTRIC FIELD DISTRIBUTION IN TANG-CAGE ............................145
BIBLIOGRAPHY .......................................................................................................................149
xi
List of Tables
2.1
General solution of Helmholtz equations (Balanis, 2005) . . . . . . . . . . . . . . .
3.1
Reaction rate constants for color change of fructose under alkaline conditions ob-
17
tained from zero order and log linear model fit to absorbance at 420 nm at 60°C,
70°C, 80°C, and 90°C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2
Dielectric properties (dielectric constant εr ’ and loss factor εr ”) of mashed potato
model food at 915 MHz in temperature range 23-100°C . . . . . . . . . . . . . . .
4.1
38
45
Dielectric properties at 915 MHz, volumetric specific heat and conductivity of
mashed potato model food measured at temperature range 25-100°C . . . . . . . .
69
4.2
Operating frequencies of MAPS generator for various power settings . . . . . . . .
77
5.1
Specific heat of mashed potatoes, peas and rice with 0-2% salt content at 60°C . . 104
5.2
Dielectric properties (dielectric constant ε′r and loss factor ε”r ) and J-T number of
mashed potatoes with 0 %, 0.1%, 0.2%, 0.5%, 1% and 2% salt content at 915 MHz
in the temperature range 60°C-121°C and L = 23 mm . . . . . . . . . . . . . . . . . 105
5.3
Dielectric properties (dielectric constant ε′r and loss factor ε”r ) and J-T number
of peas with 0%, 0.1%, 0.2%, 0.5%, 1% and 2% salt content at 915 MHz in the
temperature range 60°C-121°C and L = 18 mm . . . . . . . . . . . . . . . . . . . . 106
5.4
Dielectric properties (dielectric constant ε′r and loss factor ε”r ) and J.T. number
of rice with 0%, 0.2%, 0.5%, 1%, 1.5% and 2.0% salt content at 915 MHz in the
temperature range 60°C-121°C and L = 25 mm . . . . . . . . . . . . . . . . . . . . 107
5.5
Cold spot locations at the central layer of mashed potatoes, peas and rice samples
with 0-2% salt content; x and y represent the horizontal and vertical distance, respectively from the center of the tray . . . . . . . . . . . . . . . . . . . . . . . . . . 111
xii
5.6
Summary of results: effect of change in dielectric constant, loss factor, thickness
and volumetric specific heat on food products heated in microwave assisted thermal
sterilization (MATS)
6.1
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
Dielectric properties (dielectric constant ε’ and loss factor ε”), and J-T number of
mashed potato-gel model food with L = 18 mm, at 915 MHz in temperature range
60°C-100°C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
xiii
List of Figures
2.1
Electromagnetic and heat transfer coupling in microwave heating problems . . . .
2.2
The Yee cell for finite difference time domain numerical method (Kunz & Luebbers,
14
1993) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14
2.3
A pilot scale MATS system installed at Washington State University (Tang, 2015)
19
2.4
3-D computer simulation model for microwave assisted thermal sterilization system developed in Quickwave software; a) microwave port, (b) movement direction
of food packages, (c) food package traveling through the microwave cavity filled
with circulating hot water (Resurreccion et al., 2013; Tang, 2015) . . . . . . . . . .
2.5
The orientation of metallic temperature sensor with respect to dominant electric
field in MATS (Ey ) (Luan, Tang, Pedrow, Liu & Tang, 2013) . . . . . . . . . . . .
2.6
21
22
Validation of MATS computer simulation heating pattern using experimental results of chemical marker technique. a) computer simulation heating pattern b) experimental heating pattern in whey protein gels (Resurreccion et al., 2013) . . . . .
2.7
Effect of pH on chemical marker M1 and M3 yield (Kim, Taub, Choi & Anuradha,
1996) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1
27
(a) Mobile metallic sensor for the measurement of temperature in moving trays in
microwave assisted thermal pasteurization system and (b) its dimensions (in mm)
3.2
26
37
Temperature sensor placed at the cold spot location in the 16 oz sample tray: The
tray installed with the sensor was filled with 454 grams of model food and vacuum
packaged followed by MAPS processing for the lethality measurement . . . . . . .
3.3
37
Absorbance at 420 nm (Brown color development) measured in the model food
heated at 60-90°C for different time intervals from 2-20 minutes . . . . . . . . . .
xiv
39
3.4
First order model fit to color change kinetics of fructose in mashed potato model
food at different temperature; A=[ 1-M/M∞ ], M is absorbance at time t, M∞ is
saturation absorbance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5
Temperature (T, K) dependence of first order rate constant (k, min−1 ) of browning
reaction of fructose described by Arrhenius relationship . . . . . . . . . . . . . . .
3.6
40
41
Calculated lethality of Clostridium botulinium type E as a function of experimental
color change measured by spectrophotometric absorbance at 420 nm at (a) 60°C
(b) 70°C (c) 80°C and (d) 90°C. Linear regression coefficients and equations are
shown for each model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.7
Effect of temperature on dielectric constant of mashed potatoes model food in the
frequency range of 0.3-3 GHz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.8
43
Effect of temperature on dielectric loss factor of mashed potatoes model food in
the frequency range of 0.3-3 GHz . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.9
42
44
Effect of 30% and 20 % sucrose and 0.58%, 1.2 % , 1.8% salt addition on dielectric
constant of model food at 25°C in the frequency range of 0.3-3 GHz . . . . . . . .
46
3.10 Effect of 30% and 20% sucrose and 0.58%, 1.2%, 1.8% salt addition on dielectric
loss factor of model food at 25°C in the frequency range of 0.3-3 GHz . . . . . . .
47
3.11 Heating pattern of middle layer of model food filled in 16 oz trays obtained after
microwave processing of in MAPS a) Brown color development in mashed potato
model food b) after computer vision assistant analysis; red areas represents hot
spots and blue areas are cold spot . . . . . . . . . . . . . . . . . . . . . . . . . . . .
49
3.12 Location of cold (blue colored circle) and hot (red colored circle) spots in 16 oz
trays determined by computer vision assistant analysis; dimensions in mm . . . . .
xv
49
3.13 Absorbance values at 420 nm for different hot spots (1, 2, 3 and 4) and cold spot
(5 and 6) locations in mashed potato model food after MAPS processing at 90°C .
50
3.14 Temperature profiles and accumulated lethality measured using temperature sensors
located at hot and cold spots determined by computer vision assistant method by
analyzing browning of the mashed potato model food. Primary y axis represent
temperature (solid lines) and secondary y axis is lethality (dashed lines) calculated
for Clostridium botulinium Type E . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1
Schematic diagram for pilot scale microwave assisted thermal pasteurization system consisting of preheating, microwave heating, holding and cooling sections . .
4.2
63
Tray carrier for 10 oz trays consisting of metal frame in the middle portion (10B)
i) top view ii) front view iii) side view . . . . . . . . . . . . . . . . . . . . . . . . . .
4.6
62
Tray carrier for 10 oz trays consisting of cylindrical UltemT M bars in the middle
portion (10A) i) top view ii) front view iii) side view . . . . . . . . . . . . . . . . .
4.5
61
Tray carrier for 16 oz trays consisting of metal frame (16B) in the middle portion
i) top view ii) front view iii) side view . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4
56
Tray carrier for 16 oz trays consisting of cylindrical UltemT M bars in the middle
portion (16 A) i) top view ii) front view iii) side view . . . . . . . . . . . . . . . . .
4.3
51
64
Computer simulation model for pilot scale microwave assisted thermal pasteurization system consisting of a) one microwave cavity and tray carrier in the center
(x-axis) for the electric field analysis b) two microwave cavities and tray carrier
with food packages for heating pattern analysis . . . . . . . . . . . . . . . . . . . .
4.7
66
Total electric field distribution (E) in MAPS cavity a) empty b) in the presence of
carrier with side metal and UltemT M parts . . . . . . . . . . . . . . . . . . . . . . .
xvi
71
4.8
Electric field distribution inside the cavity when tray carrier was placed in the
center (a) 16 A (b) 16 B (c) 10 A (d) 10 B; black dashed lines represent location of
16 oz food package and 10 oz food package in sub-figure (a) and (c), respectively
4.9
72
Heating patterns in 16 oz food packages loaded into tray carrier designs a) 16 A
b) 16 B; left image is experimental heating patterns obtained by chemical marker
in model food; right image is simulation results. Areas in red and black boxes
represent hot and cold spots respectively . . . . . . . . . . . . . . . . . . . . . . . .
74
4.10 Heating patterns in 10 oz food packages loaded into tray carrier designs a) 10 A
b) 10 B; left image is experimental heating patterns obtained by chemical marker
in model food; right image is simulation results. Areas in red and black boxes
represent hot and cold spots respectively . . . . . . . . . . . . . . . . . . . . . . . .
75
4.11 Heating patterns in the middle layer of food tray for four designs of the carrier at
900, 915 and 920 MHz for carrier designs (a) 16 A (b) 16 B (c) 10 A (d) 10 B . . .
5.1
78
Schematic of a food slab immersed in water heated by 915 MHz uniform plane
waves. Electromagnetic waves are incident from top and bottom of the slab of
height L. Dielectric properties i.e. dielectric constant (ε′ ) and loss factor(ε”) of
water and food are denoted by subscripts w and f, respectively . . . . . . . . . . . .
5.2
85
Influence of food thickness (L) on power distribution along the wave propagation
direction (z) in a food with a loss factor (ε”) = 30 and dielectric constants (ε′ ) of
40 (−−), 50 ( ), 60 (⋯) and 70 (-●-) . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3
96
Influence of food thickness (L) on power distribution along the wave propagation
direction (z) in a food with a dielectric constant (ε′ ) = 50 and dielectric loss factors
(ε”) of 5 (−−), 30 (
), 100 (⋯) and 150 (-●-) . . . . . . . . . . . . . . . . . . . . .
xvii
97
5.4
Influence of dielectric properties on power dissipation profiles at the central layer
of 15 mm, 20 mm and 25 mm thick food . . . . . . . . . . . . . . . . . . . . . . . .
5.5
98
Microwave power dissipation at the central layer of a package vs J-T number for
foods with dielectric constant (ε′ )= 40 (−−), 50 (- ⋅ -), 60 (⋯) and 70 (
) and
package thickness L = 15 mm, 20 mm and 25 mm . . . . . . . . . . . . . . . . . . . 101
5.6
Temperature as a function of J-T number and volumetric specific heat at the central
layer of 18 mm thick food heated by 915 MHz microwaves for 3 minutes when incident by 1V/mm electric field on both faces for food with with dielectric constant
(ε′r )= 40 (−−), 50 (- ⋅ -), 60 (⋯) and 70 ( ) . . . . . . . . . . . . . . . . . . . . . . . 102
5.7
Temperature at the central layer of mashed potatoes (⋯), peas ( ) and rice (−−)
calculated analytically using plane wave model for 4.5 minutes of microwave heating by 915 MHz (E0 = 1V/mm on each face) . . . . . . . . . . . . . . . . . . . . . . 108
5.8
Experimental heating patterns in the central layer of (a) mashed potatoes, (b) peas,
and (c) rice samples as determined by chemical marker M2. Numbers on the top
represent the salt levels from 0-2%. Red color represents more heated areas, blue
and green represent lowest and medium heat treatments, respectively . . . . . . . . 110
5.9
Lethality (F0 ) in minutes measured experimentally as a function of salt for mashed
potatoes (▲), peas (●) and rice (∎) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
5.10 Lethality (F0 ) in minutes measured experimentally as a function of loss factor for
mashed potatoes (▲), peas (●) and rice (∎) . . . . . . . . . . . . . . . . . . . . . . . 114
5.11 Lethality (F0 ) in minutes measured experimentally for mashed potatoes (▲), peas
(●) and rice (∎) as a function of J-T number . . . . . . . . . . . . . . . . . . . . . . 115
6.1
Mashed potato model food filled in 10 oz two-compartment food packages . . . . 121
xviii
6.2
Schematic diagram of pilot scale 915 MHz single mode microwave assisted thermal
pasteurization system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
6.3
Horizontal top view of the tray carrier loaded with vacuum sealed 10 oz twocompartment food packages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
6.4
Experiment design for MAPS processing, 200 gram of food was filled in compartment A and 100 gram of food was filled in compartment B: Foods with 0%, 0.6%,
and 1.2% salt were filled in five different orientations and were processed in MAPS
using same processing schedule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
6.5
Heating patterns of trays obtained by chemical marker technique (a) case 1: 0%
salt food in both compartments, (b) case 2: 0% salt in large compartment and
0.6%in small compartment, (c) case 3: 0.6% salt in Large compartment and 0
%in small compartment, (d) case 4: 0% salt in large compartment and 1.2% in
small compartment, (e) case 5: 1.2% salt in large compartment and 0% in small
compartment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
6.6
Cold spot locations in 10 oz two-compartment trays filled with different type of
foods for (a) case 1: 0% salt food in both compartments, (b) case 2: 0% salt in
large compartment and 0.6%in small compartment, (c) case 3: 0.6% salt in Large
compartment and 0 %in small compartment, (d) case 4: 0% salt in large compartment and 1.2% in small compartment, (e) case 5: 1.2% salt in large compartment
and 0% in small compartment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
6.7
Temperature profiles at the cold spot within the single compartment 10 oz tray
filled with 0% (- ⋅ -), 0.6% ( ) and 1.2% (−−) salt model food samples . . . . . . 134
A.1 Plane wave normally incident on two interfaces of food-water . . . . . . . . . . . . 140
xix
B.1 a) Nomenclature for placement of shield according to moving directions of trays,
blue bar represent metal. Metal bars were placed on top and bottom of the tray
carriers in same orientations, b) Simulation cases, wv and wh are width of the
metal bars. gv and gh are the gap between two bars. Subscript v and h represents
vertical and horizontal orientations respectively . . . . . . . . . . . . . . . . . . . . 146
B.2 Electric field pattern without Tang-Cage . . . . . . . . . . . . . . . . . . . . . . . . 146
B.3 Electric field pattern when single vertical bar with different width (wv ) were placed
on top and bottom of the tray carriers . . . . . . . . . . . . . . . . . . . . . . . . . . 147
B.4 Electric field pattern when single horizontal bar with different widths (wh ) were
placed on top and bottom of the tray carriers . . . . . . . . . . . . . . . . . . . . . . 147
B.5 Electric field pattern when two vertical bars with different gap in between them
(gv ) were placed on top and bottom of the tray carriers . . . . . . . . . . . . . . . . 148
B.6 Electric field pattern when two horizontal bars with different gap in between them
(gh ) were placed on top and bottom of the tray carriers . . . . . . . . . . . . . . . . 148
xx
Chapter 1
INTRODUCTION
1.1
Fundamentals of thermal processing
The origin of thermal processing of packaged foods date back to 200 years ago in 1810. A french
bakery owner, Nicholas Appert developed a process of packaging food in glass containers and
heating them for a long time to preserve the food for french army for which he received an award
from french government (Appert, 1812). Although Nicholas Appert developed the first thermal
processing method, he did not know how exactly heat preservation works. The reason why heating food in sealed containers provides extended shelf life to food was explained in 1860 by Louis
Pasteur. He explained that prolonged heating kills the microorganisms responsible for the spoilage
and limited shelf life of the foods (Latour, 1993). In early 1800s, Peter Durand invented metal
canisters, followed by continuously seamed cans that replaced glass containers in the thermal processing (Farkas, 2003). After this development, food industry adopted this novel food preservation
technology very rapidly. However, first scientific studies on food safety were performed in 1895
when William Underwood, owner of a canning company started working with Samuel C. Prescott
at Massachusetts Institute of Technology (Boston). They studied time temperature effects on safety
of canned food. While performing canning operations on clams, they discovered that the clams had
heat-resistant bacterial spores, which survived the thermal processing if sufficient amount of heat
was not supplied. Those heat resistant bacteria in clam’s living environment could be killed by processing them at 250°F (121°C) for at-least ten minutes in a retort (Prescott & Underwood, 1897).
Similar time-temperature studies on other canned foods were performed by Prescott and Underwood. Their work layed foundation for the modeling of the bacterial inactivation kinetics by W.D.
1
Bigelow. Bigelow’s work set sound mathematical basis for industrial canning operations (Farkas,
2003).
1.1.1
Sterilization
Sterilization is the application of heat to a food product in order to inactivate pathogens and spoilage causing organism to have 1-2 years shelf life at room temperature. The process is designed to
destroy Clostridium botulinum type A and B proteolytic spores which is the most resistant pathogenic bacteria found in anaerobic conditions (Stumbo, 1973). This microorganism can easily grow
under anaerobic conditions and produces a toxin that is responsible for deadly food poisoning
called botulism (Smith, 1977). During sterilization, vacuum sealed foods are heated to temperatures between 110-130°C for low acid (pH > 4.6) foods to achieve 12 log reduction of Clostridium
botulinum spores (Tang, 2015).
1.1.2
Pasteurization
Pasteurization is the process to inactivate spoilage-causing enzymes, and to reduce or destroy
pathogenic & spoilage microorganisms to provide shelf life of 10 days to 6 weeks at refrigeration temperature (4 - 5°C) (Peng et al., 2017b). Currently there are no specific guidelines for the
pasteurization of food products. However the temperature and time requirements of the pasteurization process are selected based on the food composition, pH, and water activity (Peng et al.,
2017b). When the pH is below 4.5, spoilage microorganisms and enzymes are the main targets of
pasteurization. For example, the pasteurization process for orange juice is aimed at inactivating
certain enzymes such as pectinesterase and polygalacturonase (Kim, Tadini & Singh, 1999). For
high pH foods such as eggs, vegetable juices, milk and sea food, pasteurization processes are designed to inactivate vegetative pathogen bacteria such as Salmonella, Campylobacter, Escherichia
2
coli, Clostridium botulinium type E and Listeria monocytogenes (Peng et al., 2017a). Process conditions are normally selected to target 6 log reductions of bacteria by heating the product at 65 90°C for a few minutes (Holdsworth, 1997; Peng et al., 2017a). Pasteurization process is relatively
milder than sterilization and therefore sensory and nutritional characteristics of pasteurized foods
are higher quality compared to the sterilized products.
1.2
Current needs of the food industry
In modern fast-paced and busy lives, customer demands are shifting towards quick and easy meal
options at home. People want to dedicate less time to the preparation of meals. Consequently, the
consumption of ready-made meals, which were initially developed for the emergency situations
such as war field, desert, space or sea, has increased many-folds in last few decades (Gehlhar &
Regmi, 2005). The traditional techniques of canning where packaged food is heated for prolonged
period of time adversely affects the food quality and nutrition. Two alternatives for ready-to-eat
meals that are currently being used in the food industry is freezing or distributing fresh products.
Freezing provides a better quality product compared to retort, but due to formation of ice-crystals
and prolonged thawing times, frozen products also do not meet the convenience standard set by
today’s consumer. Fresh products are the best choice in terms of taste, but the short shelf life causes
food waste and high distribution cost to the producers. Microwave sterilization and pasteurization
offer benefits over conventional thermal processing methods to provide shelf stable and refrigerated high quality and clean label ready-to-eat foods (Bengtsson & Ohlsson, 1974). Microwave
pasteurized products are a good alternative in regards to shelf life problems if food manufacturers
and selling stores have the capability of distributing a refrigerated product. Microwave sterilization can deliver high quality products that can be distributed and stored at room temperature for
3
up to a year and taste good. Volumetric heating of microwaves heats the product 3-5 times faster
than conventional thermal processing systems and therefore microwave processed food retain better texture, color, taste and fresh like characteristics compared to products processed by any other
available technology (Harlfinger, 1992).
1.3
Recent developments in microwave processing of foods
According to a reputable survey in Food Engineering Magazine 1996 (Morris, 1996), microwave
energy was considered as one of the top 10 emerging food processing technologies of 21st century. Though research and academic advances has grown leaps and bounds in terms of microwave
technology for food processing, industrial adoption of the technology has been slow and very limited. Until very recently, TOP’s Foods (Olen, Belgium) was the only large food company who was
actively using microwave technology as a part of their product processing strategy. TOP’s Foods
use a technology developed by Omac (Italy) (Tang, 2015). It is an air pressurized microwave system operating at 2450 MHz which could be scaled up to 250 KPa pressure, 250 kW of power and
designed to process 2000 kg/h of product (Sun, 2014). There are some commercial microwave
pasteurization processing plants known in Europe, US and Japan for cakes, breads, and pasta. All
of these microwave ovens operate at 2450 MHz (Tang, 2015). These microwave processing systems operating at 2450 MHz frequencies have been reported to have limitations of low penetration
depth and edge heating.
In 1997, researchers in Washington State University (WSU) took a pioneering role in microwave processing research using 915 MHz frequency. At the very beginning, the project was
funded by U.S. Army Natick Soldier Center and Kraft Foods to produce shelf stable meals for
military applications as well as for the retail market (Tang, 2015). After a decade of extensive
4
research, a single-mode 915 MHz microwave cavity was developed in 2006 (Tang, Liu, Pathak
& Eugene, 2006). The most important features of WSU’s MATS technology were: a) 915 MHz
single-mode design of the microwave cavity to provide predictable and stable heating patterns for
wide range of dielectric properties of foods, and b) circulating hot water inside the cavity; dielectric properties of water closely matches with the food and thus water immersion system reduced
the edge heating effect significantly (Tang, 2015). Pilot scale microwave sterilization (MATS) and
pasteurization (MAPS) units were built for the production of high quality ready to eat meals to
evaluate the potential of the technology for catering the need of current food market. Detailed
designs of the system are discussed in the following chapters of this dissertation.
Microwave processing technology developed at WSU has become increasingly renowned
across the world over the last few years. Multiple well-known food companies, reputed universities and government agencies from the United States, Australia, and New Zealand have expressed
interest in leveraging the potential of MATS to replace traditional canning and enhance packaged
food quality. WSU arranged several hands-on boot-camps to provide MATS and MAPS training
to facilitate technology transfer from academia to the industry. R & D leaders, top management
executives from food industry and researchers from government agencies of several countries attended the boot-camps to develop and process various recipes in pilot-scale microwave processing
units. After processing, sensory evaluations were conducted to analyze texture, taste, and color
of the processed meals. Main key advantages explored by performing these pilot scale processing
and sensory evaluations were that, 1) MAPS processed meals are better in regards to quality than
current frozen or refrigerated products in the markets. In addition to the retail market, MAPS processed meals have potential to be used in cafeteria, schools, hospitals as well as restaurants; 2)
MATS processed meals are high quality and shelf stable for a year, which makes them suitable for
storage and delivery business models for online food services; 3) MATS processed meals are also
5
suitable for developing countries where cold chain distribution infrastructure is not advanced and
food safety of pasteurized products may get compromised during distribution.
MATS and MAPS technologies are maturing rapidly, and is being commercially used in certain markets worldwide. This dissertation contributes in understanding heating uniformity and
electric field distribution in the industrial designs of microwave processing systems, and provide
a general criteria for food formulations which would enhance heating efficiency and heating uniformity of packaged foods processed in single mode microwave systems.
1.4
Dissertation Objectives
This dissertation aims to:
• Provide an exhaustive literature review of simulations, modeling and validation techniques
used in microwave assisted thermal pasteurization and sterilization.
• Develop a model food based on chemical marker technique as a tool to determine heating
patterns of food processed in microwave assisted thermal pasteurization (MAPS) system.
• Build and validate computer simulation model for MAPS to study electric field distribution
and heating uniformity for novel designs of stainless steel food tray carriers.
• Develop and validate a metric for qualitative estimation of relative heating rates of various
food formulations processed in MATS and MAPS.
• Analyse the change in heating patterns of foods affected by the salt content in multi-compartment
trays during MAPS processing.
6
1.5
Dissertation Organization
This dissertation is organized into seven chapters. In the first chapter, an overview of thermal processing, traditional processing methods and introduction to microwave assisted thermal processing
have been presented along with the scope of the dissertation. The second chapter provides insight
into the most common numerical techniques and software used for electromagnetic modeling of
microwave heating processes in the food industry. It also discusses the challenges faced in development and validation of the previous simulation models for pilot scale microwave processing
units. In the third chapter, the focus is on developing a model food system for MAPS system. The
model food was developed as a tool to validate computer simulations. The fourth chapter presents
evaluation of novel way to transport food inside the cavity on the heating uniformity of MAPS
processing. The fifth chapter presents analytical 1-D model to analyze heating of a rectangular
dielectric slab with top and bottom 915 MHz incidence. The analytical results and validation tests
are used to represent the effect of food formulations on power dissipation in MAPS and MATS as a
single number. Heating patterns analysis of two-compartment trays when two foods with different
dielectric properties are heated together is presented in the sixth chapter, and the seventh chapter
provides insights and inferences gained from this research work. It also includes concluding remarks and an outlook for future work.
7
Chapter 2
MODELING AND COMPUTER SIMULATIONS IN MICROWAVE ASSISTED
THERMAL PROCESSING
2.1
Abstract
Microwave assisted thermal sterilization/pasteurization (MATS and MAPS) is a FDA accepted
food processing technology developed at Washington State University. During MATS/MAPS processing, hot water is combined with electromagnetic waves to achieve uniform volumetric heating
of packaged foods in 915 MHz single mode cavities. The technology has great potential for the
food processing industry to provide high quality ready-to-eat meals. Computer simulations have
played an important role in understanding, designing and enhancing efficiency of these single mode
microwave systems. This chapter presents a literature review on modeling and numerical techniques used in microwave heating of foods, with specific focus on simulation models developed
for microwave assisted thermal sterilization system (MATS). It also summarizes the techniques
and challenges in validating the modeling and simulations of these complex microwave heating
systems.
2.2
Introduction
Simulations and modeling are effective tools that enables us to visualize and interpret an invisible
physical phenomena described by hard-to-imagine mathematical formula. Microwave heating of
foods is one such complex phenomena. Physics of microwave propagation is governed by space
and time dependent Maxwell’s equations (Sadiku, 2010). Simulations and modeling of microwave
heating systems, based on Maxwell’s equations, help us to evaluate various scenarios that can
8
happen during food processing. It enables us to analyze the effects of factors such as cavity designs,
food properties, frequency and input power on the heating efficiency of foods. Simulations and
modeling guide the design of the microwave heating systems at the earliest stages of development,
reducing operating costs and testing times. However it is critical, for accuracy of results, that while
modeling we do not make unrealistic assumptions so as to violate the physical laws that govern the
phenomena. In the following sections, we will discuss the basic physics of microwave heating and
techniques used in simulations and modeling of microwave systems.
2.3
Maxwell’s equations coupled with heat transfer
The behaviour of electromagnetic phenomena is described by a set of equations known as Maxwell’s equations (Balanis, 2005; Sadiku, 2010). Microwaves are electromagnetic waves with
wavelength in the range 0.001-0.3 m and thus physics of microwave heating is governed by Maxwell’s equations. Microwave energy interaction with a material depends on the electric and magnetic field distributions within the object. The field distributions within a food product is a function
of incident frequency, input microwave power, microwave cavity dimensions, dielectric properties
and geometry of food (Barringer, Davis, Gordon, Ayappa & H.T, 1995). To obtain the electric and
magnetic field distributions within an object of interest, Maxwell’s equations are solved. Differential form of Maxwell’s equations is the most widely used representation (Balanis, 2005):
▽ × E⃗ = −Mi −
⃗
∂B
∂t
(2.1)
⃗
⃗ = J⃗ + ∂ D
▽×H
∂t
(2.2)
⃗ = qev
▽.D
(2.3)
⃗ = qmv
▽.B
(2.4)
9
⃗ is the magnetic field intensity (Amperes/m),
where E⃗ is the electric field intensity (Volts/m), H
⃗ is the electric flux density (Coulombs/m2 ), B
⃗ is the magnetic flux density (webers/m2 ), qev is
D
the electric charge density (Coulombs/m3 ), qmv is the magnetic charge density (webers/m3 ), J is
the electric current density (Amperes/m2 ) and M is the magnetic current density (Volts/m2 ). For a
material with linear material constitutive laws, flux densities are defined as:
⃗ = εE⃗
D
(2.5)
⃗ = µH
⃗
B
(2.6)
J⃗ = σ E⃗
(2.7)
where ε, µ and σ are permittivity, permeability, and electrical conductivity, respectively. Maxwell’s
equations are first order coupled partial differential equations. This means that each equation has
more than one unknowns, i.e. unknown electric and magnetic fields appearing in each equation.
Such equations do not have closed form solutions for complex and irregular geometries (Balanis,
2005); the magnetic and electric field expressions can not be evaluated in a finite number of operations. In such cases, numerical approach is used to obtain the solutions. Closed form solution and
numerical solutions are both possible in finite number of standard operations but closed form is
an exact solution whereas numerical solution is an approximation. Therefore two approaches are
available to obtain field distributions from Maxwell’s equations for a given boundary conditions
i.e. 1) Numerical methods such as finite difference time domain are used to obtain approximation
to close form solutions for coupled Maxwell’s equations, 2) Maxwell’s equations are uncoupled
to a second order partial equation known as wave equation, and wave equations are solved either
analytically (for simple geometries) or by numerical methods such as finite element methods (for
complex and irregular geometries).
10
After obtaining field distribution in the material, dissipated power within the object is computed using Poynting theorem as (Balanis, 2005):
P = 2πf ε0 ε”ef f E 2 + 2πf µ0 µ”ef f H 2
(2.8)
where f is incident frequency (Hz), ε”ef f is overall dielectric loss factor of food, µ”ef f is magnetic
loss factor, E is electric field intensity and H is magnetic field intensity. In the heating of dielectric
materials such as food, it is assumed that magnetic field does not contribute to the heating and µef f
is non-significant.
The dissipated power computed from equation 2.8 is used as input in heat transfer equations
to obtain predictive models to estimate heating profiles within the food products. The coupled
electromagnetic and heat transfer mathematical model is given as (Datta, 1990):
∇2 T −
ρCp ∂T 1
Ð
→
+ 2πf ε”ef f ∣ E ∣2 = 0
k ∂t k
(2.9)
where medium properties thermal conductivity (k), specific heat (C) density (ρ) and dielectric loss
(ε”) are functions of temperature. The coupled electromagnetic and heat transfer equations are
solved using numerical methods for various food geometry and microwave cavity dimensions.
2.4
Numerical methods in microwave heating
For the vast majority of geometries and problems of microwave processing, Maxwell’s equations
cannot be solved using analytical methods. Instead, different types of discretizations are applied
to construct an approximation of the partial differential Maxwell’s equations. These discretization
methods convert the partial differential equations (PDEs) into linear set of equations, which are
easy to solve using numerical methods (Chew, Michielssen, Song & Jin, 2001). These solution
to the linear set of Maxwell’s equations are approximations of the real solution to the Maxwell’s
11
equations. The accuracy and matching of these approximation to exact close form solution of
Maxwell’s equations depend on the chosen discretization schemes.
The numerical simulation of a microwave heating problem is a two step process involving
solution to Maxwell’s and heat transfer equations. In the first step, Maxwell’s equations are solved
to obtain electric field intensities and microwave power dissipation. In the second step, power term
is used as source in the heat transfer equations to obtain temperature at any instant of time. Food
permittivity which affects the space and time variation of the electromagnetic field, is a function
of temperature. Similarly thermal properties such as density, specific heat and thermal conductivity are also a function of temperature. Thus in next step, the food properties are updated and
the Maxwell’s equations are solved again for field intensities for next time step. The procedure is
repeated for the assigned duration of microwave heating (figure 2.1). The commercial softwares
such as QuickwaveT M (QWED, Poland), ANSYS (Ansys, Pennsylvania, USA), and COMSOL
(COMSOL multiphysics, Sweden) use the same approach of modeling heat transfer and Maxwell’s equations, but they differ in the choice of numerical method. Finite difference time domain
(FDTD) method, finite element method (FEM), geometric theory of diffraction and method of moments (MOM), transmission line method (TLM), Boundary element method (BEM) are used for
computational electromagnetic. Specifically for microwave heating problems, FEM and FDTD are
the two most popular methods which have been used in past rigorously (Celuch & Kopyt, 2009).
2.4.1
Finite Element method
Finite element method is a implicit numerical approach where a linear system of Maxwell’s equations is solved through either matrix inversion or iterative methods (Bathe & Wilson, 1976; Ames,
2014). FEM give solutions in the frequency domain, and the accuracy of the solutions is increased
by increasing mesh density. In FEM, computational volume is divided into smaller quadrilaterals
12
or triangles in two dimensions or tetrahedral and octahedral in three dimensions. This discretization gives a set of linear Maxwell’s equations. Analytical Solution to those equations is not
challenging but discretization of volume in million of cells makes it impractical to solve directly.
Thus iterative methods are used to solve these equations (Risman & Celuch-Marcysiak, 2000).
Commercial softwares which uses FEM are ANSYS (Ansys, Pennsylvania, USA), and COMSOL
(COMSOL multiphysics, Sweden). Softwares based on FEM requires relatively more computer
memory and simulation time due to the unavoidable matrix operation. Therefore these softwares
are appropriate for small size systems such as domestic microwave oven (Pitchai, 2011).
2.4.2
Finite difference time domain
Finite difference time domain (FDTD) method is an explicit numerical method, where coupled
Maxwell’s equations are solved directly in differential form rather than individual wave equations
for electric and magnetic field (Kunz & Luebbers, 1993). FDTD is a modified form of finite
difference methods, in which discretization is performed based on Yee’s algorithm, using central
difference approximation technique (Taflove & Hagness C., 1995). Figure 2.2 shows Yee’s unit
⃗ and magnetic field (H)
⃗ components are arranged in three dimensional
cell where electric field (E)
space in such a way that each electric field is surrounded by four circulating magnetic field vector
and vice versa. This arrangement allows discretization of time dependent partial differential Maxwell’s equations using central-difference approximations to the space and time partial derivatives.
The resulting finite-difference equations are solved in either software or hardware in a leapfrog
manner. The electric field vector components at any point are solved at a given instant in time;
then the magnetic field vector components at same point are solved at the next time step and the
process is repeated until the electromagnetic field behavior is fully evolved.
13
Figure 2.1: Electromagnetic and heat transfer coupling in microwave heating problems
Figure 2.2: The Yee cell for finite difference time domain numerical method (Kunz & Luebbers,
1993)
14
In explicit numerical approaches such as FDTD, the Courant-Friedrichs-Lewy (CFL) condition is a necessary condition for convergence of the solution. The condition states that the temporal
step (∆t) must be less than a certain time in computer simulations, otherwise the simulation will not
produce correct results. The condition is named after scientists Richard Courant, Kurt Friedrichs,
and Hans Lewy who described it in 1928. Courant number (S) is the ratio of distance of energy
propagation in temporal step to spatial step size. Since energy should not propagate more than one
spatial step in one time step, Courant number should be less than 1 to produce correct results in
FDTD simulations (Kunz & Luebbers, 1993):
S=√
2.5
c△t
(△x) + (△y) + (△z)
2
2
(2.10)
2
Analytical solutions to Maxwell’s equations
Analytical solutions to Maxwell’s equations are obtained in simplified scenarios and for problems
possessing symmetry. The key steps in obtaining analytical solutions of Maxwell’s equation are; 1)
to convert coupled differential equations to uncoupled second order Maxwell’s equations, referred
to as wave equations, 2) Convert wave equations to scalar Helmholtz equations for each coordinate
and obtain solutions to each of the Helmholtz equation, 3) Examine the geometry in the problem
and form a general solution by combining Helmholtz equations and, 4) Apply boundary conditions
to obtain the specific solution to the problem.
Wave equations are obtained by combining equation 2.1, 2.2, 2.3 and, 2.4 to eliminate either
Ð
→
Ð
→
of the unknown field. Vector wave equations for electric field ( E ) and magnetic fields ( H ) are
given as:
Ð
→
Ð→
Ð
→ 1
Ð
→
Ð
→
▽2 E = ▽ × Mi + jωµ Ji + ▽ qve + jωµσ E − ω 2 µε E
15
(2.11)
Ð
→
Ð
→
Ð
→
Ð
→
Ð→
Ð→ 1
▽2 H = − ▽ × Ji + σ Mi + jωεMi + ▽ qvm + jωµσ H − ω 2 µε H
µ
(2.12)
For homogeneous, source free medium the wave equations equations are simplified to:
Ð
→
Ð
→
▽2 E⃗ = −ω 2 εµE⃗ + jωµσ E = γ 2 E
(2.13)
→
Ð
→
⃗ = −ω 2 εµH
⃗ + jωµσ Ð
▽2 H
H = γ2 H
(2.14)
γ 2 = jωµσ − ω 2 µε
(2.15)
γ = α + jβ
(2.16)
where
where α and β are attenuation constant (Np/m) and phase constant (rad/m) respectively. α, β and
γ are functions of dielectric properties, conductivity and frequency. In rectangular coordinates, a
general solution to total electric field can be written as:
E⃗x,y,z = aˆx Ex + aˆy Ey + aˆz Ez
(2.17)
Combining equations 2.13 and 2.17, vector wave equations are converted to three scalar Helmholtz
equations for each of the coordinate:
▽2 Ex = −γ 2 Ex
(2.18)
▽2 Ey = −γ 2 Ey
(2.19)
▽2 Ez = −γ 2 Ez
(2.20)
The three scalar equations are of the same form so if solution to one of them is obtained, other
two can be formed following the same steps. General solutions to these equations can be obtained
using separation of variables method, where electric field is written in the form:
Ex = f (x) × g(y) × h(z)
16
(2.21)
Equation 2.21 is substituted into equation 2.18 and general solution to the resulting differential
equation is obtained. Different valid solutions listed in table 2.1 satisfy the equations 2.18, 2.19,
and 2.20. Although all of the solutions listed in table 2.1 are valid for functions f (x), g(y) and
h(z), the most appropriate solutions are chosen after examining the geometry of the problem in
question and behaviour of waves. A reference analytical solution using this approach for a problem
considering two side plane wave incidence on a rectangular slab is shown in the Appendix A.
Table 2.1: General solution of Helmholtz equations (Balanis, 2005)
Wave type
Wave function
Traveling waves
e−jβz for + z travel
ejβz for - z travel
Standing waves
cos(βz) or sin(βz) for ± z
Evanescent waves
e−αz for + z
eαz for - z travel
cosh(αz) or sinh(αz) for ± z
e−jγz for + z travel
Attenuating traveling waves
ejγz for - z travel
Attenuating standing waves
cos (γz) or sin (γz) for ±z
Several authors have used these analytical techniques to analyse microwave heating problems.
One of the most common model is called Lambert’s law which is a solution to wave equation
assuming exponential decay of the plane wave within the sample. In Lambert’s law, electric field
17
intensity decays inside the sample as per:
Ez = E0 e−αz
(2.22)
Where α is attenuation factor and 1/α is known as penetration depth where electric field intensity
reduces to 1/e of that at the surface. However many authors have compared Lambert’s law with
exact solution to Maxwell’s equations in various food shapes and sizes, and unanimously agreed
that complete Maxwell’s equations should be solved for accurate solutions to power profiles in
microwave cavities (Barringer et al., 1995; Ayappa & Davis, 1991; Oliveira & Franca, 2002; Campanone & Zaritzky, 2005; Datta, 1990; Dibben, 2001a; Yang & Gunasekaran, 2004). Maxwell’s
equations predict the power term, heat generation, and dissipation, incorporating reflections at the
front, back and all internal surfaces. While solving Maxwell’s equations rigorously wave interactions are included so that standing wave patterns are calculated and the electric field distribution
and power dissipation is evaluated.
2.6
Simulation and modeling of microwave assisted thermal
processing systems
Microwave assisted thermal sterilization and pasteurization systems (MATS and MAPS) are pilot
scale units governed by complex principles of physics involving hot water heating, electromagnetic heating, and translational movement of the food along the cavity. Therefore, FDTD based
commercial software Quickwave was the best choice in terms of memory requirements and time
to simulate the MATS system. One of the simulation studies at early stages of MATS development
was performed by Pathak, Liu and Tang (2003). The simulation model was built in Quickwave
18
and was used to characterize the dimensions of a single mode rectangular cavity for 915 MHz incidence. They also compared the power dissipation in food when it was placed in water vs air, and
concluded that if cavity was filled with water more homogeneous power distribution was obtained
(Pathak et al., 2003). The results were validated by heating a whey gel model food and analyzing heating profile by infra red camera. Based on these preliminary results and after conducting
several experiments, a single mode water immersion system was designed for the sterilization of
foods (Tang et al., 2006) (figure 2.3).
Figure 2.3: A pilot scale MATS system installed at Washington State University (Tang, 2015)
Chen, Tang and Liu (2007) developed a simulation model for the MATS system considering top and bottom incidence of 915 MHz in a single cavity to analyse temperature profiles in
food loads. Early versions of Quickwave was equipped with a basic heat transfer module which
allowed modeling of conduction within the food. However the software did not provide flexibility to simulate convection heating by circulating water in MATS cavity which was crucial for
19
accurate temperature profiles. Thus for simulation of single mode 915 MHz cavity filled with water, Quickwave results were coupled with an external code to model heat transfer processes. The
power generated by electromagnetic fields was computed in Quickwave. The power term was then
used as input for heat transfer model which generated the temperature information. Whey protein
gel was used as a model food to study the experimental heating pattern using chemical marker
technique. There were some mismatch in simulated temperature and experimental temperature,
this was attributed to placement of sensor and fluctuations in surrounding water temperature. Also
the MATS system had continuous operation with moving food trays, while in simulations only
stationary food tray was considered (Chen et al., 2007).
Later, Chen, Tang and Liu (2008) simulated food movement by changing location of food
trays. Temperature distribution calculated at one location was used as the initial conditions of the
food for the next location. Such arrangement required less memory allocation during the simulation and could be possible with the disk storage options available in the year 2008. In later
years, new version of Quickwave software was launched which had additional features and allowed movement of food as well as to set convection boundary conditions within the software.
With these improvements in the software and availability of larger memory disks, Resurreccion
et al. (2013) built MATS-computer simulation model (CSM) (figure 2.4).
MATS-CSM was more flexible with respect to mesh, geometries and movement speed. The
model was validated by experiments on whey protein gels. The validated MATS-CSM model was
further used to analyse the effect of operating frequency fluctuations around 915 MHz (902-928
MHz) on heating patterns of foods (Resurreccion et al., 2015b). Simulation results showed that the
locations of cold and hot spots were not affected by the frequency. However the temperature difference between the cold and hot spots increased as the operating frequency increased (Resurreccion
et al., 2015b).
20
Figure 2.4: 3-D computer simulation model for microwave assisted thermal sterilization system
developed in Quickwave software; a) microwave port, (b) movement direction of food packages, (c) food package traveling through the microwave cavity filled with circulating hot water
(Resurreccion et al., 2013; Tang, 2015)
In the continuous operation of MATS, metallic mobile sensors were preferred over optical
fiber sensors to measure the temperature at cold spots. Optical fiber sensors requires connection
to a light source outside the cavity which is impractical in moving food packages in pressurized
cavity (Tang, 2015). Therefore it was necessary to study the performance of metallic sensors during
the processing in MATS. Luan, Tang, Pedrow, Liu and Tang (2013) studied the influence of metal
sensors and orientation on the temperature readings. The results were validated by chemical marker
technique. It was observed that if sensors are placed at 90° angle to the dominant electric field as
shown in figure 2.5, the temperature readings were not influenced by the presence of sensors.
21
Figure 2.5: The orientation of metallic temperature sensor with respect to dominant electric field
in MATS (Ey ) (Luan, Tang, Pedrow, Liu & Tang, 2013)
MATS simulation model was also used to analyze the influence of metal sensors in high
electric field systems (24 kW/cavity) which is possible in industrial scale high power systems
(Luan, Tang, Pedrow, Liu & Tang, 2015b). They observed that high power zones are created
near the tip of the metal sensors in high electric field intensity systems which can be reduced
by choosing proper geometry and size of the sensors. A spherical shape tip with diameter less
than 2 mm was recommended to be used for MATS high intensity industrial scale systems (Luan
et al., 2015b). Further simulations were conducted to analyze the electric field patterns inside the
microwave cavity and wave guide of MATS system. It was anticipated that by changing dimensions
of microwave cavity in y direction it was possible to obtain relatively more uniform heating patterns
22
(Luan, Tang, Pedrow, Liu & Tang, 2016). Based on these results, a pilot scale microwave heating
system was designed for microwave assisted thermal pasteurization system MAPS. MAPS was
designed to operate in lower temperature range and employed a different way to transport food
inside the cavity.
The quickwave computer simulation models of MATS have significant contribution in understanding, analyzing, designing and improvising the systems over the last decade. Quickwave
software has advantages of using FDTD approach which requires relatively less memory and time
compared to FEM based softwares such as COMSOL. Since MATS is a large pilot scale unit, even
after employing FDTD approach the computing time for pilot scale MATS system is 42 hours as
reported by Resurreccion et al. (2013). Quickwave is a windows based software which requires a
physical key and it is not possible to connect it to high performance computing resources which
are normally operated by linux. Thus for large memory systems it becomes difficult and time exhaustive to use computer simulations to study influence of various factor. For example to analyse
the effect of change in dielectric properties on temperature profiles at cold spot location, simulations should be run for each value of dielectric properties separately, making the use of simulation
models impractical for such applications. Analytical models developed, using correct boundary
conditions and assumptions, may provide insightful information in analyzing the qualitative influence of parameters such as dielectric properties or thickness. Analytical models can be solved
using less time consuming softwares such as MATLAB or OCTAVE. Till now, there are no analytical models developed for MATS or MAPS.
23
2.7
Validation techniques for MATS simulation models
To establish the credibility of a computer model, it is critical to validate the results of simulation
using experimental techniques. Only after validation, the model can be trusted to analyze the
phenomenon which are not possible to study experimentally. In continuous systems such as MATS,
it was not possible to use techniques available for domestic microwave ovens such as infra red
imaging to validate the heating pattern results. Also it was impractical to use fiber optic sensors
for temperature validation studies (Tang, 2015). Thus new techniques were established for the
measurement of temperature profiles and heating pattern determination.
2.7.1
Heating pattern validation
Kim, Taub, Choi and Anuradha (1996) proposed chemical markers M1, M2 and M3 as time temperature indicators for high temperature short time processing applications. These chemical markers are intermediate products of maillard reactions between reducing sugars and amino acids and
have been used successfully to map heating intensity in various thermal processing (Nott & Hall,
1999; Gentry & Roberts, 2004; Gupta, Mikhaylenko, Balasubramaniam & Tang, 2011; Wnorowski
& Yaylayan, 2002).
For MATS, chemical marker M2 was found most suitable for the heating pattern determination tests (Pandit, Tang, Mikhaylenko & Liu, 2006; Lau et al., 2003b; Wang, Lau, Tang &
Mao, 2004). D-ribose was used as precursor for the marker M2 formation (Tang et al., 2008).
Yield of chemical marker M2 was determined using HPLC at various locations which was directly
correlated to the lethality achieved in the food at those locations (Pandit et al., 2006). However
determination of marker yield using chromatography techniques in 3D food packages time consuming. As reported by Pandit et al. (2006), to analyze heating pattern by measuring chemical
24
marker M2 yield at 40 evenly distributed points in one 10 oz tray of mashed potato model food
required, two persons and 2.5 days. Thus a new method of heating pattern determination was proposed by Pandit, Tang, Liu and Mikhaylenko (2007b) based on the color change of the sample due
to Maillard reaction. It was established that browning of foods due to microwave processing was
directly correlated to the lethality of the sample (Pandit et al., 2006). The method was based on
a computer software which converts the image of processed food into thermal image using RGB
values (Pandit et al., 2007b) and based on the largest and lowest color values, hot and cold spots
were located. This was an excellent advancement in studying heating pattern. The technique of
analysing heating pattern based on color change eliminates the need to measure marker yield using
HPLC at various location in 3D food packages.
For heating pattern determination using computer vision assistant technique, a major requirement is to develop a model food that (1) change color during the short time microwave processing,
(2) has firm texture which is easy to cut in different layers vertically and horizontally, (3) is opaque
to avoid interference in color analysis of each layer and , (4) has dielectric properties similar to
food. Mashed potato model food and whey protein gels with added D-ribose were used to study
heating patterns in MATS (Resurreccion et al., 2013; Pandit et al., 2006; Pandit et al., 2007b;
Resurreccion et al., 2015b; Luan et al., 2015b; Luan et al., 2013). The chemical marker heating
patterns obtained experimentally had close agreement with simulation results as shown in figure
2.6.
25
Figure 2.6: Validation of MATS computer simulation heating pattern using experimental results
of chemical marker technique. a) computer simulation heating pattern b) experimental heating
pattern in whey protein gels (Resurreccion et al., 2013)
The model food systems developed for MATS processes (100-121°C) have slow reaction
rates at pasteurization temperature (70-90°C), making them unsuitable for MAPS. Therefore, a
new gellan gel model food was developed to study heating pattern in MAPS Zhang, Tang, Liu,
Bohnet and Tang (2014). D-ribose was combined with Lysine to enhance the marker formation at
lower temperature and obtain detectable color changes. However, this model food based on marker
M2 and gellan gel had limitation of being transparent and expensive due to high cost of lysine.
Kim et al. (1996) had proposed another way to enhance the reaction rate of marker formations by
changing pH of system. They reported that chemical markers M1 and M3 were formed in high pH
conditions but yield of marker M3 decreased with increasing pH while chemical marker M1 yield
increased with increasing pH up-to 10 and decreased after that (figure 2.7). M1 is formed naturally
in vegetables under high temperature processing. Therefore addition of fructose to a vegetable
matrix can be added to increase the yield of M1 further at pasteurization temperatures (Kim et
26
al., 1996). This makes the fructose-based chemical marker a commercially viable alternative to
D-ribose and lysine based expensive approaches.
Figure 2.7: Effect of pH on chemical marker M1 and M3 yield (Kim, Taub, Choi & Anuradha,
1996)
2.7.2
Temperature profile validation
Validation of temperature profile of simulation results is much more challenging than heating pattern validations. Several factors such as frequency fluctuations, circulating water temperature,
temperature and frequency dependence of dielectric and thermal properties of food, must be taken
into account while simulating temperature profiles of food. But including all of these factors at the
same time in the simulations is almost impossible due to inherent limitations of either softwares
or experimental measurements. For example, while simulating a microwave heating problem in
Quickwave, a single frequency waveform is excited and corresponding temperature profiles are
27
evaluated. But in practice, the magnetron produces a spectrum of frequency. The range of frequency can vary with age, type, brand or power settings of the magnetron (Resurreccion et al.,
2015b). Power dissipation as well as dielectric properties of food are function of frequency, and
thus experimental temperature profile is a result of heating caused by a range of magnetron frequency spectrum. Similarly food properties such as density, thermal conductivity, dielectric constant, loss factor are function of temperature. Although it is possible to input temperature dependence of food properties in Quickwave software, the experimental values involve some deviation
due to instrumental errors and thus average values of food properties are used in the computation,
which can lead to differences in simulations and experimental temperature profiles.
2.8
Knowledge gaps
The aim of this research was to develop sound mathematical tools to evaluate the electric field distributions, heating patterns, and heating efficiency of foods affected by designs of the food carriers,
different size of the food packages or food formulations in MATS and MAPS processing. In order
to achieve this goal, this project addressed several knowledge gaps: (1) Model food appropriate
for pasteurization temperature and compatible with existing computer vision assistant technique
for the heating pattern determination (2) A validated computer simulation model to study heating
uniformity in new designs of the stainless steel food carriers used in industrial scale systems (3)
Analytical model for qualitative comparison of heating rates of foods affected by change in dielectric and thermal properties; special focus was given that in addition to accuracy, the calculations
are less time consuming, and are practical to use while developing recipes and processing schedule
for MAPS and MATS.
28
Chapter 3
APPLICATION OF NON-ENZYMATIC BROWNING OF FRUCTOSE FOR HEATING
PATTERN DETERMINATION IN MICROWAVE ASSISTED
THERMAL PASTEURIZATION SYSTEM
3.1
Abstract
Various model foods and chemical markers have been used for the heating pattern determination in
microwave processing at sterilization temperature (110-130°C). These chemical marker systems
have slow reaction rates at pasteurization temperature (70-90°C). In this study, non-enzymatic
browning of fructose under alkaline conditions is investigated for its suitability to be used in heating pattern determination of microwave assisted thermal pasteurization. Kinetics of browning of
fructose in mashed potato model food were studied. The model food samples were heated in a
water bath at 60°C, 70°C, 80°C, and 90°C for different time intervals and the browning kinetics
was studied by spectrophotometry measurements at 420 nm. Reaction rate kinetics was fit to linear
first order kinetic model. Application of this model food to determine heating pattern in microwave
assisted thermal pasteurization system was demonstrated. Dielectric properties of the model food
were measured to determine its suitability as a model food. Sucrose and salt were used as effective
additives for the adjustment of the dielectric constants and loss factor respectively of the mashed
potato. This system offers advantages of being cost-effective, opaque, homogeneous and easy to
handle and thus provides an excellent system to locate the hot and cold spot of the food products.
29
3.2
Introduction
Introduction of the FDA Food Safety Modernization Act (FSMA), 2011 has increased academic
and industry-wide interest in novel pasteurization technologies. In this regard, microwave processing is a promising thermal preservation technique for a variety of food products as it offers
volumetric heating and short time exposure of high temperature (Tang, 2015). A pilot-scale 915
MHz single mode microwave assisted pasteurization system (MAPS) has been developed at Washington State University that can be scaled up to process food products at 70-90°C in food processing plants for control of bacterial and viral pathogens. The design of the system ensures
repeatable and predictable heating patterns in pre-packaged foods.
Determination of the location of cold spot is a critical step in developing process schedules
in order to ensure food safety. Temperature sensors would have been the first choice to determine the heating patterns of the food processed by MAPS. However, implementation of sufficient
numbers of sensors in moving food packages without altering the heating pattern in a microwave
system is very challenging. Kim et al. (1996) suggested using Maillard reaction products as chemical indicators of lethality for high-temperature short time processing. Proposed chemical markers M1(2,3-dihydro-3,5-dihydroxy-6-methyl-4(H)-pyran-4-one), M2(4-hydroxy-5-methyl-3(2H)furanone) and M3(5-hydroxymethyl-furfural) are intermediate products of final brown pigments
compounds produced due to the thermal processing of foods containing reducing sugars (Martins,
Jongen & Boekel, 2000). However, it is a time-consuming process to study heating patterns in 3D
food packages via quantitative measurement of marker yields using analytical methods. With advancements in digital imaging technology, a novel method based on the irreversible color change
of the food during thermal processing was developed to visualize the intensity of heat treatment
throughout the food package (Pandit et al., 2007b). Heating patterns obtained by this technique
30
(Pandit et al., 2006; Lau et al., 2003a) are combined with single point temperature measurements
and computer simulations (Chen et al., 2008; Chen et al., 2007; Resurreccion et al., 2013) to validate the temperature distribution and develop processing schedule of microwave processing at
sterilization temperatures (Luan et al., 2015b; Tang, 2015).
Model food systems developed for sterilization processes (110-130°C) (Lau et al., 2003a;
Pandit et al., 2007b; Ross, 1993; Ramaswamy, Awuah, Kim & Choi, 1996; Wang, Wig, Tang &
Hallberg, 2003) are not suitable for pasteurization (70-90°C) applications due to the slower reaction
kinetics. Previous research on development of model food for pasteurization temperatures is very
limited focusing only on Maillard reaction of ribose and lysine. A preliminary work conducted
on the comparison of mashed potato, gellan gel and egg white gel model foods pointed out the
limitations of egg white and gellan gel model food for heating pattern determination using image
analysis (Bornhorst, Tang, Sablani & Barbosa Cánovas, 2017). The main limitations of these
model foods are that high temperature (70°C) exposure to form a gel, long preparation time and
firm texture which is difficult to cut after processing. Therefore, a new model food system that is
easy to prepare and cost-effective is required for pasteurization temperature process.
Fructose is a reducing sugar which participates in Maillard reaction. It is known to undergo
faster degradation reactions at higher pH of about 8-12 leading to faster browning rates (Ajandouz,
Tchiakpe, Dalle Ore, Benajiba & Puigserver, 2001; Shaw, Tatum & Berry, 1968) even without
presence of amino acids (Shaw et al., 1968; Shaw, Tatum & Berry, 1971; Ledl, Schnell & Severin,
1995). Fructose in alkaline conditions undergoes an equilibrium via 1,2 and 2,3- enediol anion species, known as Lobry de Brujn-Alberda van Ekenstein rearrangement. The enediol intermediate
undergoes non-reversible degradation reactions, including β elimination, benzylic-acid rearrangements and aldol condensation reactions, with subsequent formation of brown pigments (Eggleston
& Vercellotti, 2000).
31
Thus, the objectives of this study were: (i) to investigate the formation of brown pigments
via fructose degradation under pasteurization conditions in order to correlate the color change
with intensity of thermal processing; (ii) to validate the application of the new model system in
heating pattern evaluation of the MAPS process using computer vision method; and (iii) To adjust
dielectric properties of the new model food to match wide range of food products.
3.3
Materials and Methods
3.3.1
Food preparation and thermal treatment
Mashed potato model food was prepared by mixing 20% dry potato flakes (Oregon Potato Company, WA) and 1.8% fructose in 1 M sodium hydroxide solution.1.5 grams of model food was
heated at 60°C, 70°C, 80°C, and 90°C in thermal cells described in Zhang et al. (2014). The
come-up time (CUT), defined as the time for the coldest spot in the sample to reach within 0.5°
of the target was measured to be 1.5-2 min using a calibrated type-T thermocouple. After heating
samples were taken out at the intervals of 2, 5, 10, 15 and 20 minutes and were cooled down using
an ice bath to stop the further reaction. The heating time of the sample was measured excluding CUT. After heating, model food samples were mixed in 10 ml of water and centrifuged for 10
minutes at 8000 rpm. The supernatant was used for further measurements. For dielectric properties
measurement, salt and sugar were added to the water along with fructose and sodium hydroxide
followed by mixing in the dried potato flakes. The initial pH of the model food was measured to be
11 which was not affected by the addition of salt or sucrose. All the experiments were conducted
in triplicates.
32
3.3.2
UV absorbance and browning
UV-vis measurement was performed using a Pharmacia Biotech (Cambridge, England) Ultrospec
4000 spectrophotometer. Brandtech disposable UV-transparent Cuvettes were used. Appropriate
dilutions were made in order to obtain absorbance values less than 1.5. Absorbance value at 420
nm were used as indicator of brown color development during the reaction (Ajandouz et al., 2001).
Readings were multiplied by the dilution factor for the further analysis.
3.3.3
Modelling procedure
It is known that any reagent or chemical reaction which follows a nth order kinetics and a rate constant that follows the Arrhenious equation can be used for mapping heating uniformity in thermal
processing (Ramaswamy et al., 1996; Hendrickx, Weng, Maesmans & Tobback, 1992). Thus,
experimental data obtained by spectrophotometric measurements at 420 nm was fitted to the following reaction kinetics equation as described by previous researchers (Kim et al., 1996; Pandit
et al., 2007b).
dM
= k[T (t)](M − M∞ )n
dt
(3.1)
where M is absorbance at time t, M∞ is the absorbance at saturation and k is the rate constant
at the processing temperature. M∞ is defined as the point after which there is no effect of further
heating on the browning intensity. To obtain the saturation color absorbance value (M∞ ), samples
were heated for 60 minutes at 60, 70, 80 and 90°C and then treated in the same manner as described
above. For fructose browning reaction, (n = 0) zero order and (n = 1) first order kinetics fit was
evaluated using Minitab 12. Statistical parameters of regression (R2 and S) were obtained directly
from the software. The standard error of regression (S) value represents the average deviation of
the experimental data from the regression line. It must be <= 2.5 to produce a sufficiently narrow
33
95% prediction interval. The lower the value of S, the more precise is the regression. For zero
order, equation (1) has the solution of the form:
M (t) = kt
(3.2)
A first order differential equation has the solution of the form (Kim et al., 1996; Ross, 1993)
M (t) = M∞ [1 − e−kt ]
(3.3)
Plotting of log[ 1-M/M∞ ] vs time gives a straight line with a slope equal to the first order rate
constant.
3.3.4
Food properties measurement
In microwave heating, dielectric properties are principal parameters which determines how the
energy is absorbed and distributed inside a food material and hence can affect the heating pattern
(Tang & Resurreccion, 2009). Dielectric properties are described by complex relative permittivity
(ε∗r ) which has two components relative dielectric constant (ε′r ) and relative dielectric loss factor
(ε”r ).
ε∗r = ε′r − jε”r
(3.4)
√
where j= −1. The dielectric constant reflects the energy storage capability when electromagnetic energy is incident on the material, and loss factor is associated with the conversion of
electromagnetic energy into thermal energy used for heating the food (Wang et al., 2003). Effect
of salt on dielectric properties at 0.58%, 1.2% and 1.8% concentration and sucrose at 0.2 g/ml and
0.3 g/ml was studied. The criteria for choosing salt levels was based on the recommended levels
in MAPS processing to obtain the optimum penetration depth (Guan, Cheng, Wang & Tang, 2004;
Zhang et al., 2015). Dielectric constant is mainly a function of water content (Luan et al., 2015a;
34
Zhang et al., 2015). Therefore the purpose of adding 0.2 g/ml and 0.3 g/ml sucrose was to reduce
the water content to 60 % and 50 % respectively.
Dielectric properties were measured using an HP 8752 C Network Analyzer and 85070B
Open-End Coaxial Dielectric Probe (Agilent Technologies, Santa Clara, CA) in the microwave
frequency range: 0.3-3 GHz. The measurements were carried out at temperatures of 23°C, 30°C,
40°C, 50°C, 60°C, 70°C, 80°C, 90°C, and 100°C. All measurements were conducted in triplicate.
3.3.5
Microwave assisted thermal pasteurization (MAPS) processing
A pilot scale MAPS system has four sections viz, preheating, microwave heating, holding and
cooling. The microwave heating section consists of two rectangular cavities connected to a 915
MHz generator. The details of the design of the single mode cavities for the heating section is
described by Tang (2015).
For processing, the food samples were filled in 16 oz trays (160 mm x 125 mm x 16 mm),
vacuum sealed and kept at 4°C overnight for MAPS treatment. The trays were placed on a patent
pending carrier and moved horizontally inside the cavity. The preheating water, circulating water
in the cavities, holding section and cooling temperature were set at 61°C, 93°C, 93°C, and 23°C
respectively. Food in 16 oz trays was pre-heated for 30 minutes, heated in the microwave section
with a residence time of 2.8 minutes, and then the food trays were moved to the holding section
for 5 minutes. The samples were cooled down in the cooling section for 5 minutes and unloaded.
3.3.6
Heating pattern determination by computer vision assistant
After processing, the mashed potato food was kept at 4°C overnight. Due to the symmetrical design
of the MAPS system, the vertical location of the cold spot is in the middle layer of the food (Zhang
et al., 2014). The location of cold spot at middle layer was also validated by the temperature
35
measurements and computer simulations (Resurreccion, 2012; Luan et al., 2015b). Therefore the
food was cut horizontally in middle and the images were taken using a camera set-up described
previously by Pandit et al. (2007b). The analysis of the images was done by Adobe Photoshop
and computer vision assistant technique (Pandit et al., 2006). The software divided the whole food
sample image into various grids and based on the lowest and highest color values exact location
of the cold and hot spot was determined. The software converted the most heated parts of the
processed model food in red color (hot regions) and least heated to blue color (cold spot). Areas
which received the medium amount of thermal energy were converted to other colors between blue
and red. All experiments were performed in duplicates.
3.3.7
Temperature profile
To validate the location of cold and hot spots determined by browning reaction, PICO-VACQ 1Tc
mobile metallic temperature sensors manufactured by TMI-Orion (Castelnau-le-Lez, France) were
used as shown in Figure 3.1. Presence of metal temperature sensors in a food package could create
high temperature zones near the tip of the sensors, caused by interaction of electric field with the
probe tip. Therefore sensors with a spherical tip placed perpendicular to the dominant electric field
component (Ey ) were used to reduce the distortion of electric fields (Luan et al., 2015b), as shown
in Figure 3.2.
The trays were filled with 454 g of mashed potato model and vacuum-sealed (100 mbar)
with lid films (sealing conditions: 200°C for 4 seconds dwell time) with a vacuum sealer (Multivac T-200, Multivac Inc., Kansas City, MO, U.S.A.). Samples were processed using 7 KW total
microwave power and a tray speed of 13.5 mm/s. This speed provided 2 minutes of microwave
heating. The microwave heating was followed by hot water heating in the holding section for
10 minutes at 90 °C. Finally, all trays were cooled in the cooling section at 23 °C. The process
36
was designed to achieve a desired lethality for a 6 log reduction of psychrotrophic non-proteolytic
Clostridium botulinum type B and E at the cold spot. Sensors were taken out after the processing
and data were recorded. The cumulative lethality (P) was calculated using following equation:
t
P = ∫ 10(T −Tref )/z dt
0
(3.5)
Tref is 90°C and z value is 9.84°C.
(a)
(b)
Figure 3.1: (a) Mobile metallic sensor for the measurement of temperature in moving trays in
microwave assisted thermal pasteurization system and (b) its dimensions (in mm)
Figure 3.2: Temperature sensor placed at the cold spot location in the 16 oz sample tray: The tray
installed with the sensor was filled with 454 grams of model food and vacuum packaged followed
by MAPS processing for the lethality measurement
37
3.4
Results and Discussion
3.4.1
Browning kinetics
The absorbance values at 420 nm in figure 3.3 shows that in general browning increased with time
and temperature. The browning at 60°C and 70°C increases linearly with time (zero order R2 =
0.98). However at 80°C and 90°C, exponential behaviour is observed. Table 3.1 shows zero order
and first order rate constants with regression coefficients. At all temperatures accuracy (R2 value)
of first order model was either better or equal to the zero order kinetics. Therefore, first order rate
constants were considered for the further analysis.
Table 3.1: Reaction rate constants for color change of fructose under alkaline conditions obtained
from zero order and log linear model fit to absorbance at 420 nm at 60°C, 70°C, 80°C, and 90°C
T(°C)
Zero order Kmax (min-1 )
R2
1st order Kmax (min-1 )
R2
60
0.020
0.98
0.030
0.98
70
0.077
0.98
0.041
0.99
80
0.160
0.83
0.102
0.99
90
0.129
0.68
0.291
0.98
Figure 3.4 shows first order (equation 3) fit to brown color development in the process of
fructose degradation at 60°C, 70°C, 80°C, and 90°C. S value of 0.035, 0.037, 0.102 and 0.408
were obtained at 60°C, 70°C, 80°C and 90°C respectively. In all cases, S values were much less
than 2.5%, which shows the accuracy of fitting to the linear model.
38
3.5
3
Absorbance at 420 nm
2.5
2
1.5
1
0.5
0
0
5
10
15
20
Time (minutes)
90°C
80°C
70°C
60°C
Figure 3.3: Absorbance at 420 nm (Brown color development) measured in the model food
heated at 60-90°C for different time intervals from 2-20 minutes
Temperature dependence of rate constant of browning reaction was fitted to Arrhenius type
equation with a R2 value 0.98, giving activation energy (Ea ) of 76.6 kJ/mol (Figure 3.5). This
value matches with the range reported in the literature for non-enzymatic browning in fruits and
vegetables (16-30 kcal/mol)(Labuza & Baisier, 1992). The activation energy of browning obtained
in this work was in the range of activation energies cited for chemical markers used in microwave
processing. A range of 81.4-96.1 kJ/mol for chemical marker M2 in mashed potato model food
(Pandit et al., 2006) and 81.5 kJ/mol in whey protein gels (Lau et al., 2003a) have been reported in
39
the literature. Wang et al. (2004) reported activation energy of M1 formation in whey protein gel
and broccoli extract in the range of 85.6-120.9 kJ/mol.
6
a) R² = 0.9748
-ln[A]
5
4
3
2
b) R² = 0.9880
c) R² = 0.9944
1
d) R² = 0.9825
0
0
5
10
15
20
Time (minutes)
90°C
80°C
70°C
60°C
Figure 3.4: First order model fit to color change kinetics of fructose in mashed potato model food
at different temperature; A=[ 1-M/M∞ ], M is absorbance at time t, M∞ is saturation absorbance
40
4.0
3.5
3.0
-ln [k]
2.5
Ea= 76.6 kJ/mol
R² = 0.98
2.0
1.5
1.0
0.5
0.0
0.0027
0.0028
0.0029
0.0030
1/T
Figure 3.5: Temperature (T, K) dependence of first order rate constant (k, min−1 ) of browning
reaction of fructose described by Arrhenius relationship
3.4.2
Color and lethality correlation
Plots of calculated lethality versus experimental absorbance values obtained at 60, 70, 80, and 90°C
are shown in Figure 3.6. Lethality was calculated using equation 3.5. R2 > 0.97 at all temperature
shows significant linear relationship between browning and lethality. Positive correlation suggests
that lower lethality was achieved at lower absorbance value. Therefore, it can be deduced that
areas with lower concentration of brown pigments had received lower amount of thermal energy
and vice versa.
41
0.020
0.20
0.018
0.18
0.016
0.16
0.14
y = 0.0291x + 0.0014
R² = 0.9825
0.012
Lethality (minutes)
Lethality (minutes)
0.014
0.010
0.008
0.006
y = 0.1599x + 0.0071
R² = 0.9944
0.12
0.10
0.08
0.06
0.004
0.04
0.002
0.02
0.00
0.000
0
0.1
0.2
0.3
0.4
0.5
0.6
0.0
0.7
0.2
0.4
0.6
-ln (A)
-ln (A)
2.5
25
2.0
20
1.5
y = 0.8897x - 0.029
R² = 0.988
1.0
1.0
1.2
(b)
Lethality (minutes)
Lethality (minutes)
(a)
0.8
0.5
15
y = 3.3399x - 0.2315
R² = 0.9748
10
5
0.0
0
0.0
0.5
1.0
1.5
2.0
2.5
0
-ln (A)
(c)
1
2
3
-ln (A)
4
5
6
7
(d)
Figure 3.6: Calculated lethality of Clostridium botulinium type E as a function of experimental
color change measured by spectrophotometric absorbance at 420 nm at (a) 60°C (b) 70°C (c) 80°C
and (d) 90°C. Linear regression coefficients and equations are shown for each model
42
3.4.3
Dielectric properties of model food
MAPS is designed to process food products such as vegetables, fruits, pasta, meat and dessert,
which have broad range of dielectric properties (Wang et al., 2003; Wang, Tang, Rasco, Kong &
Wang, 2008; Peng, Tang, Barrett, Sablani & Powers, 2014). It is essential for model foods to have
matching dielectric properties with food products in order to evaluate and validate the temperature
distribution within the foods.
70
Increasing temperature
Dielectric constant
65
60
55
50
45
0.3
1.2
25
30
40
Frequency ( GHz)
50
60
70
2.1
80
3.0
90
100
Figure 3.7: Effect of temperature on dielectric constant of mashed potatoes model food in the
frequency range of 0.3-3 GHz
43
100
90
Dielectric loss factor
80
70
60
50
Increasing temperature
40
30
20
10
0.3
1.2
25
30
40
Frequency ( GHz)
50
60
70
2.1
80
3.0
90
100
Figure 3.8: Effect of temperature on dielectric loss factor of mashed potatoes model food in the
frequency range of 0.3-3 GHz
Figures 3.7 and 3.8 show dielectric constant and loss factor of model food changing with
temperature and frequency. The dielectric constant of mashed potato model food decreased with
temperature as well as frequency. The declining of constant was more at higher temperature (>
70°C ). The effect of frequency and temperature on loss factor is more complex: the loss factor
increased with temperature upto 1.2 GHz. For frequencies in the range of 1.2-2.1 GHz, slight
increase was observed for temperatures 50-100°C. At higher frequencies in the range of 2.1-3
GHz no significant difference was observed in the loss factor at all temperatures. With frequency,
44
in the range from 0.3 GHz to 1.2 GHz there is a sharp decrease; however, at higher frequencies
the loss factor does not change significantly. A similar trend of dielectric properties of food has
been reported by many researchers in past (Guan et al., 2004; Luan et al., 2015b; Zhang et al.,
2015). This phenomenon is attributed due to the two types of contribution in loss factor i.e. ionic
and dipolar. Ionic dielectric loss factor has a linear relationship with conductivity and frequency,
and dominates at lower frequencies. However, the dipole contribution due to polarization of water
molecules dominates at the higher frequencies (Zhang et al., 2015). Dielectric constant and loss
factor values at 915 MHz obtained at the measured temperature range is listed in Table 3.2.
Table 3.2: Dielectric properties (dielectric constant εr ’ and loss factor εr ”) of mashed potato model
food at 915 MHz in temperature range 23-100°C
T(°C)
ε′r
ε”r
25
63.1 ±2.0
19.1 ± 0.9
30
62.4±2.1
20.5± 1.2
40
61.6± 2.4
21.8± 0.8
50
61.1±2.1
23.8± 0.9
60
60.5±1.7
26.4± 1.0
70
59.9±1.4
29.2± 0.5
80
58.4±0.5
32.1± 0.1
90
56.9±0.2
34.1± 0.3
100
54.8±1.0
35.8± 0.2
The effect of salt and sucrose addition on dielectric constant and loss factor of the new model
food in the frequency range 0.3-3 GHz at 25°C are shown in Figures 3.9 and 3.10, respectively.
45
70
Dielectric constant
60
50
Effect of salt
40
30
Effect of
sucrose
20
10
0.3
1.2
No additive
1.80% salt
2.1
Frequency ( GHz)
0.58% salt
20% Sucrose
3.0
1.20% salt
30% Sucrose
Figure 3.9: Effect of 30% and 20 % sucrose and 0.58%, 1.2 % , 1.8% salt addition on dielectric
constant of model food at 25°C in the frequency range of 0.3-3 GHz
46
120
100
Dielectric loss factor
80
60
Increasing salt content
40
20
Increasing sucrose content
0
0.3
1.2
No additive
1.80% salt
2.1
Frequency ( GHz)
0.58% salt
20% sucrose
3.0
1.20% salt
30% sucrose
Figure 3.10: Effect of 30% and 20% sucrose and 0.58%, 1.2%, 1.8% salt addition on dielectric
loss factor of model food at 25°C in the frequency range of 0.3-3 GHz
The presence of 0.56% salt reduced the value of ε′ from 63.1 to 56 at 915 MHz but it did not
change further by increasing the salt concentration to 1.2% and 1.8%. A significant decrease in the
dielectric constant (at 915 MHz and 25°C) from 63.1 to 40 and 32 was observed by the addition of
sucrose at 20% and 30% respectively. This effect could have been caused by the lower amount of
water content in the model food or due to the binding of sugar-water molecules. As shown in Figure
47
3.10, addition of 20% sucrose did not have any effect on the loss factor; but when adding 30%, ε”
decreased slightly. This could be either due to the lower amount of water or increase in viscosity
of the sample which reduced the ion mobility. Increasing salt amount in the food increases the
loss factor (at 915 MHz and 25°C) from 17 at 0% to 28, 40, and 47 at 0.56%, 1.2% and 1.8%
respectively. This increase was attributed to the conduction contribution in the loss factor. These
values are similar to those reported by Guan et al. (2004) in their studies for mashed potatoes. An
increase in salt content from 0.8% to 2.8% in mashed potatoes caused a slight increase in dielectric
constant from 64 to 62, but increased the loss factor from 27.1 to 52.4, at 915 MHz and 20°C
(Guan et al., 2004). Slight lower values of loss factor obtained in this work is due to the different
amount of salt contents used in the preparation.
3.4.4
Application of the mashed potato model food in MAPS processing
A clear heating pattern in 16 oz trays based on browning of mashed potato model food after processing in microwave assistant pasteurization system was obtained. Four symmetrically located
hot zones (areas which received the highest amount of thermal energy) and two cold zones (which
received the lowest amount of thermal energy) (Figure 3.11) were observed. Figure 3.12 shows
the location of cold and hot spots detected by the computer vision method. In order to validate
results of the computer vision method for the new model system for MAPS process, samples from
the middle layer of the processed food from point 1, 2, 3, 4 and 5 were taken and absorbance was
recorded. Figure 3.13 shows the absorbance at 420 nm taken at locations 1, 2, 3, 4, 5 and 6. Absorbance at locations 1, 2, 3 and 4 are higher than the absorbance at locations 5 and 6. This finding
confirms the result of the computer vision assistant method, that locations 1, 2, 3 and 4 received
higher thermal energy than the locations 5 and 6. Among hot spots, the number 1 location gave the
highest browning value whereas for the cold spot, location 6 gave the lowest.
48
Figure 3.11: Heating pattern of middle layer of model food filled in 16 oz trays obtained after
microwave processing of in MAPS a) Brown color development in mashed potato model food
b) after computer vision assistant analysis; red areas represents hot spots and blue areas are cold
spot
Figure 3.12: Location of cold (blue colored circle) and hot (red colored circle) spots in 16 oz
trays determined by computer vision assistant analysis; dimensions in mm
49
2.0
1.8
1.6
1.4
-ln[A]
1.2
1.0
0.8
0.6
0.4
0.2
0.0
1
2
3
4
Location number
5
6
Figure 3.13: Absorbance values at 420 nm for different hot spots (1, 2, 3 and 4) and cold spot (5
and 6) locations in mashed potato model food after MAPS processing at 90°C
Temperature profiles at the hot (location 1) and cold (location 6) spots were recorded using
mobile metallic temperature sensors. The sensors were installed in a metallic protective tube and
a rubber cushion was used to set the height of the tip at middle layer of the food. The sensor was
fixed in the middle layer so that the tip is located at the predetermined hot and cold spots locations.
The temperature at the hot spot was always higher than the temperature at the cold spot. This
ensures the reliability of the computer vision method for the accurate determination of hot and
cold spots in this new model food during MAPS processing at 90°C.
50
100
Preheating
MW
Holding
Cooling
60
90
50
80
40
60
50
30
40
20
30
20
Lethality (min)
Temperature ( °C)
70
10
10
0
0
0
10
20
30
40
50
60
Time (min)
Temperature at cold spot (°C)
Temperature at hot spot (°C)
P_90 at cold spot
P_90 at hot spot
Figure 3.14: Temperature profiles and accumulated lethality measured using temperature sensors
located at hot and cold spots determined by computer vision assistant method by analyzing
browning of the mashed potato model food. Primary y axis represent temperature (solid lines)
and secondary y axis is lethality (dashed lines) calculated for Clostridium botulinium Type E
Figure 3.14 shows a time temperature profile obtained in MAPS system using temperature
sensors installed at the hot and cold spots. However, converting absorbance values quantitatively
predicted lethality (P90 ) of 6 and 3.5 minutes at the hot and cold spots, respectively, which was
51
lower than the temperature sensor measurements. The possible reason for this discrepancy was
that the model food was kept overnight in refrigeration for easy cutting. That might have led to
the diffusion of pigments from higher concentration areas to lower concentration. Similar stability
challenge was observed for the chemical marker M2 concentration in egg white model food (Zhang
et al., 2014) and M1 formation in meat beads (Ramaswamy et al., 1996). Small time gap between
processing and evaluation of the absorbance will help in reducing the estimation errors. In view
of these possible experimental errors, we believe that further calibration of the model food is
required for the exact quantitative calculation of lethality using brown pigments. However this
model system can successfully be used to map the intensity of heating received by the food and
determine the locations of hot and cold spots, where there are no viable alternatives available.
3.5
Conclusion
In this paper, non-enzymatic browning of fructose and its applicability in determination of heating
patterns of microwave assisted thermal pasteurization process was evaluated. First order log linear
kinetics was used to describe color change in mashed potato model food with time and temperature,
and first order rate constant showed Arrhenius type temperature dependence. Addition of salt and
sucrose was used to adjust the dielectric loss factor and constant of the food, respectively. This
model food in combination with single point temperature measurements will be used to predict
and evaluate the heating patterns and develop the processing schedules for wide variety of food
products. It would also serve as a heating pattern validation tool for a computer simulation model
of the MAPS system.
52
Chapter 4
EVALUATION OF FOOD CARRIER DESIGNS TO IMPROVE HEATING UNIFORMITY IN MICROWAVE ASSISTED THERMAL PASTEURIZATION
USING COMPUTER SIMULATIONS
4.1
Abstract
Microwave transparent materials such as plastics and polymers have been used to carry the food
packages in microwave processing systems. However, polymers and plastics may have a short
life in the high-temperature environment and thus may not be desirable in an industrial setting.
Microwave assisted thermal pasteurization system (MAPS) is a food processing technology that
employs carriers made from stainless steel to move pre-packaged foods inside a 915 MHz single
mode microwave cavity. This paper studied the performance of metal carriers for 10 oz and 16
oz food packages in the MAPS. A computer simulation model built with Quick-wave software
was developed to characterize the food carrier designs. Computer simulations were validated using mashed potatoes model food processed in a pilot scale MAP system; heating patterns of the
samples were detected by a chemical-marker based computer vision method. The results demonstrated that the MAPS with moving metal carriers has predictable and uniform heating patterns.
Results showed that different designs of the food carriers could be used to modify electric field
distribution to obtain relatively uniform heating patterns within the cavity. Simulation results also
illustrated that magnetron frequency variations do not affect the heating patterns of food packages processed using new designs of carriers. The simulations and experiments conducted in this
work showed that metal carriers are a novel, effective and durable mechanism for transporting
pre-packaged foods in microwave heating systems.
53
4.2
Introduction
Microwave assisted thermal pasteurization (MAPS) is a novel technology developed at Washington State University for pasteurization of pre-packaged food products. The technology is based
on simultaneous heating of food by microwaves and hot water (Resurreccion et al., 2013). This
combination heating results in shorter processing time than conventional surface heating methods,
and hence better quality of food products (Tang, 2015). One of the main challenges in microwave
processing is the non-uniform heating. Thus it is possible that the food at the hot spot locations
may be overcooked in order to achieve the required lethality for the food at the cold spot. Nonuniform microwave heating becomes major challenge in large scale industrial systems where high
microwave power is used for the processing. Therefore, for the commercialization of the technology, low temperature differences between hot and cold spots are highly desirable to improve the
food quality.
Single mode cavity design and circulating water inside the MAPS cavity provides flexibility
for placing and moving different types of materials including metals inside the cavity (Tang & Liu,
2017). Specially designed tray carriers made up of rectangular thin metal sheets, and cylindrical
shape Polyetherimide (PEI) parts were used to distribute the electric field evenly and provide uniform heating of the food samples for 10 oz and 16 oz food packages (Tang & Liu, 2017). By
changing designs of these food package carriers, the heating pattern was altered for different size
of food packages to obtain higher heating uniformity. Use of stainless steel in designing the carriers
for food packages also resists corrosion in water immersion system and adds durability.
It is important to understand the electric field pattern inside the MAPS cavity and how the
presence of carriers modify the heating profiles. The information will enable to improve the heating
uniformity in MAPS system using various designs of food package carriers. Till now there are no
54
effective sensors for the accurate measurement of electric field in high permittivity materials such
as food. Therefore, in this study, a computer simulation model was developed to explore the
electric field patterns in pilot scale MAPS as affected by the presence of food package carriers.
This work aimed to study the various designs of the food carriers which can be used effectively
to modify electric field patterns to create uniform heating in MAPS system. In this work four
different types of food carrier designs suitable for 10 oz and 16 oz food packages were studied using
computer simulations. For the validation, fructose based chemical marker in the mashed potatoes
was used (Jain, Wang, Liu, Tang & Bohnet, 2017a). The chemical marker technique is based on the
browning reaction of reducing sugars in a model food and has been used effectively to study heating
patterns in microwave assisted thermal processing (Pandit, Tang, Liu & Mikhaylenko, 2007a; Luan
et al., 2013; Luan et al., 2015b; Zhang et al., 2015; Resurreccion et al., 2013; Resurreccion et al.,
2015a).
4.3
Materials and Methods
4.3.1
Computer simulation procedure
(a) MAPS physical system: The pilot scale MAPS system consists of four sections, i.e., preheating, microwave heating, holding and cooling. Each section contains water at different
temperature, e.g., preheating at 61°C microwave, and holding at 75-95°C and cooling at
25°C. Microwave heating section consists of two connected rectangular cavities which are
connected to a generator. A detailed description of 915 MHz single mode cavity is described
by Tang (2015). The food packages are placed in a carrier and moved inside the cavity on a
set of wheels. The residence time of the food inside the cavity is controlled by the speed of
moving carrier. Figure 4.1 shows schematic of the pilot scale MAPS unit.
55
56
microwave heating, holding and cooling sections
Figure 4.1: Schematic diagram for pilot scale microwave assisted thermal pasteurization system consisting of preheating,
(b) Simulation software: In this study, Quick-wave 3D (QW-3D, QWED, Poland) version 7.5,
an electromagnetic simulator based on finite difference time domain method was used. QW3D editor was used to creating the geometry of the MAPS system, mesh generation and
specification of the simulation parameters (e.g., frequency, power). After the geometry was
built, QW-simulator with basic heat transfer module (BHM) was used for the calculation and
analysis of electromagnetic and heat transfer parameters. To ensure accuracy and efficiency,
non-uniform mesh was generated with maximum cell size of 4 mm x 4 mm x 18 mm in the
air and 4 mm x 4 mm x 1 mm in water and food according to the 10 points per wavelength
rule (Resurreccion et al., 2013).
(c) Finite difference time-domain (FD-TD) governing equations: Physics of electromagnetic
wave propagation is described by set of Maxwell’s equations, which can be written in integral
form as (Balanis, 2005):
⃗ = − d ∫ ∫ B.
⃗
⃗ dl
⃗ ds
∮c E.
dt
s
(4.1)
⃗ + ∫ ∫ (J⃗i + J⃗c ).ds
⃗
⃗ = d ∫ ∫ D.
⃗ ds
⃗ dl
∮c H.
dt
s
s
(4.2)
⃗ = Qe
⃗ ds
∯s D.
(4.3)
⃗ =0
⃗ ds
∯s B.
(4.4)
⃗ is the magnetic field, D
⃗ is the electric flux density, B
⃗ is
where E⃗ is the electric field, H
the magnetic flux density. Qe is the electric charge enclosed by surface S. C is a contour
path surrounding the surface S. Ji and Jc are source current density and conduction current
density, respectively. Flux densities are defined as:
⃗ = εE⃗
D
(4.5)
⃗ = µH
⃗
B
(4.6)
57
where ε and µ are permittivity and permeability respectively. These set of equations were
solved by quickwave software using conformal FDTD technique which is explained in detail
by Taflove and Hagness C. (1995).
(d) Initial and boundary conditions:
(i) Preheating section of MAPS allows the food to reach uniform temperature before the
food enter the microwave cavity. In this study the initial temperature of the food was set
to be 61°C, circulating hot water temperature was set at 93°C. Temperature of circulating
hot water in MAPS system was constant due to continuous flow of the water. (ii) For this
study, 8.7 kW total power was applied. The power was assumed to be equally divided among
the two cavities and power for each cavity was evenly distributed to two ports (figure 4.1).
Electromagnetic dissipated power is related to electric field intensity by following equation
(Dibben, 2001b):
P = 2π f ε0 ε”r ∣E∣
2
(4.7)
where f is frequency Hz, ε” is loss factor, ε0 is permittivity of air (8.85 × 10−12 F/m) and ∣E∣
is electric field magnitude (V/m). (iii) Only solid and semi-solid food were considered where
dominant heat transport mode within the food was conduction following the conduction heat
transfer equation (Dibben, 2001b):
▽2 T −
ρCp ∂T
=0
k ∂t
(4.8)
where ρ is density (kg/m3 ), Cp is specific heat (kJ/kg-K) and k is thermal conductivity of food
(W/m-K). (iv) At the food and water boundary, heat flux (q) was governed by convective heat
transfer (Bergman & Incropera, 2011),
q = h(T − Ts )
58
(4.9)
where h is convective heat transfer coefficient (W/m2 -K), T is food temperature in °C, and Ts
is circulating water temperature in °C. Prior to microwave heating simulations, heat transfer
coefficient calculations were performed. Experiments were conducted in MAPS to record
the temperature profile history at the cold spot when microwave power was switched off.
The capacitance lumped method was used to approximate the value of heat transfer coefficient (Bergman & Incropera, 2011). Convective heat transfer coefficient (h) between hot
circulating water and food packages was set at 190 W/m2 K.
(e) Food properties measurement: Dielectric properties of mashed potato model food in the
range of 300-3000 MHz was measured using Hewlett-Packard 8752C network analyzer (Palo
Alto, CA 94304). The measurements were carried out at temperatures of 22, 30, 40, 50, 60,
70, 80, 90, and 100°C using the procedures reported in Zhang et al. (2015), Zhang et al.
(2014). Mashed potato sample was filled in a cylindrical test cell and temperature of the
sample was controlled by circulating oil to the gap between two walls of the test cell from an
oil bath. All measurements were conducted in triplicate. Double needle probe KD2 (Decagon Devices Inc, Pullman, WA) was used to measure the thermal conductivity, diffusivity,
specific heat of the samples in the temperature range 25-100 °C. A Dual needle (SH-1), 30
mm long, 1.28 mm diameter probe with 6 mm spacing between needles was used. The KD2
probe was carefully inserted into the food sample inside the test cell. The dielectric properties of the food at 915 MHz and thermal properties were input in the simulation program as
a function of temperature.
4.3.2
Food carrier designs
Carrier designs for the processing of 10 oz [90 (x) × 135 (y) × 25 (z) mm] and 16 oz [160 (x) ×
125 (y) × 25 (z) mm] food packages were investigated in this study. The side part of all the carriers
59
was made up of Polyetherimide (UltemT M ) and rectangular metal plates of specific thicknesses
as shown in figures. 4.2, 4.3, 4.4 and, 4.5. UltemT M is a microwave transparent material and
was also used in a microwave assisted thermal sterilization (MATS) system to alter the electric
field distribution within the cavity (Chen et al., 2008). In the MATS system, rectangular slabs of
UltemT M of various thickness were attached to the cavity walls which helped in controlling the
heating patterns (Resurreccion et al., 2013). Similar rectangular slabs of UltemT M was used in the
pasteurization system (MAPS). However, instead of fixing the UltemT M to the cavity wall, it was
attached to the food carriers which moved through the cavities. For the food holding part of the
carriers, two designs were studied to scatter and distribute the electric field evenly inside the food
package. 1) evenly spaced cylindrical UltemT M rods were added on the carriers as shown in figure.
4.2 and 4.4. Tray carriers for 16 and 10 oz food packages were fixed with four and seven cylindrical
rods, respectively. A plastic mesh with suitable sized pockets for 10 and 16 oz packages was used
to secure the food packages in place. This design is referred as 16 A and 10 A tray carriers for
16 and 10 oz food packages, respectively. 2) A 6.3 mm thick metal frame along the edges of the
food packages was employed in the second design (figure 4.3 and 4.5). The food packages were
attached to the carriers using a clip. The metal frame used in the system had perforations to allow
the flow of circulating hot water. This design is referred as 16 B and 10 B tray carriers for 16 and
10 oz food packages, respectively. 16 A or 16 B carriers could carry 3 packages at a time while 10
A or 10 B could carry 6 packages at once.
60
(i)
a
b
b
b
b
a
(ii)
b
b
b
b
a
b
(iii)
b
b
b
a
Metal
b
a
Ultem
Figure 4.2: Tray carrier for 16 oz trays consisting of cylindrical UltemT M bars in the middle
portion (16 A) i) top view ii) front view iii) side view
61
(i)
b
a
b
(ii)
b
b
b
a
b
(iii)
b
b
b
a
Metal
b
a
Ultem
Figure 4.3: Tray carrier for 16 oz trays consisting of metal frame (16B) in the middle portion i)
top view ii) front view iii) side view
62
(i)
a
b
b
b
b
b
b
b
a
(ii)
b
b
b
b
a
b
b
(iii)
b
b
b
a
Metal
b
a
Ultem
Figure 4.4: Tray carrier for 10 oz trays consisting of cylindrical UltemT M bars in the middle
portion (10A) i) top view ii) front view iii) side view
63
b
(i)
b
b
a
a
(ii)
b
b
b
a
(iii)
b
b
b
a
Metal
b
a
Ultem
Figure 4.5: Tray carrier for 10 oz trays consisting of metal frame in the middle portion (10B) i)
top view ii) front view iii) side view
64
4.3.3
Electric field distribution and heating pattern analysis
For all four designs (10 A, 10 B, 16 A and 16 B), computer simulations were used to study electric
field distribution and heating patterns of food packages. The pilot scale MAPS system had two
connected rectangular cavities operating in single mode with same electric field distribution in
each of them. The electric field distributions within the cavities change continuously as the tray
carrier moves through the cavities during the processing. However, in this study the steady state
electric field distributions were analyzed with tray carrier placed in center of one cavity (figure
4.6a). Most of the microwaves propagate through the food when the location of package is aligned
with the top and bottom horn (i.e. at middle of the cavity). Thus the power dissipation occurring
inside the food when the food package is in the center of the cavity (along x axis) will dominate
the heating patterns. Therefore, one cavity was simulated to analyze the electric field patterns in
the following cases: (1) empty cavity (2) side part of the carriers in the center of one cavity and,
(3) whole tray carrier at the center of one cavity.
For heating pattern determination, both cavities were simulated to estimate the temperature
differences between hot and cold spots inside food at the end of the process (figure 4.6b). In the
operation of MAPS system, packages moved at the speed of 14.8 mm/s in the x-y plane. For the
entire length of the two microwave cavities, the residence time for a package to move through the
two microwave heating cavities was 1.7 minutes. To study the heating pattern, the translational
movement was incorporated in the simulation model using built-in mechanism along a step-wise
linear trajectory in the x-y plane, which requires a definition of heating time per time step. The
choice of heating time (∆t) at each step is very critical for the convergence and efficient use of the
computation resources. Too large ∆t may cause computation errors and too small will increase
the computation time. Therefore after performing a heating time sensitivity tests as explained by
65
Resurreccion et al. (2013) for 8, 16 and 32 steps to optimize the time and accuracy of the model.
16-time steps with each step having heating of 6.5 seconds was used to incorporate the movement
of the tray carrier.
(a)
(b)
Figure 4.6: Computer simulation model for pilot scale microwave assisted thermal pasteurization system consisting of a) one microwave cavity and tray carrier in the center (x-axis) for the
electric field analysis b) two microwave cavities and tray carrier with food packages for heating
pattern analysis
66
4.3.4
Validation experiment procedure
Fructose browning in mashed potato model food was used as chemical marker for the experimental
validation of heating pattern as described by Jain et al. (2017a). Model food samples were prepared
by adding 4% dried potato flakes and 1% gellan gel in water at 90°C. The mixture was kept at 90°C
and stirred continuously. Heating was stopped when a homogeneous solution was obtained. When
temperature of the mixture dropped down to 70°C, 0.4% liquid titanium dioxide and 1.5% fructose
were added. Solution was cooled further to 65°C and 0.1% sodium hydroxide and 0.3% calcium
chloride was added and mixed for one minute. The solution was then poured into the trays and
was allowed to set for 1-2 hours in a refrigerator. The food samples were then vacuum packed, and
loaded in the food carrier.
MAPS process schedule was selected to achieve a lethality for a 6 log reduction of psychrotrophic non-proteolytic Clostridium botulinum type E (P90○ C = 10 minutes) at cold spot in the
model food (Peng et al., 2017a). Model food samples were placed on the carriers and were loaded
in the preheating section at 60°C in the pilot scale MAPS system. After 30 minutes, model food
packages were moved to the microwave heating section at a speed of 14.8 mm/second for 1.7
minutes of heating in the two microwave cavities. Temperature of circulating water in the microwave cavity was set at 93°C. Samples were then kept in holding section for 280 seconds and
then they were moved to cooling section at 25°C. After cooling down food packages were unloaded
from the system. The heating pattern of the food packages were determined using the computer
vision assistant techniques as described by Pandit et al. (2007a). The formation of brown pigments
follows first order reaction kinetics similar to bacterial death kinetics (Zhang et al., 2014; Jain et
al., 2017a), and therefore browning intensity is directly related to the lethality (Pandit et al., 2006).
For further validation, mobile metallic temperature sensors (TMI-Orion, Castelnau-le-Lez,
67
France) were placed at the cold and hot spot locations determined by the computer vision assistant
method. Mashed potato model food was filled in the trays and was processed in the MAPS system
as described above. Temperature sensors were placed perpendicular to the electric field component
as suggested by Luan et al. (2013). The cumulative lethality (P) was calculated from the recorded
temperature data using following equation (Holdsworth, 1997):
t
P = ∫ 10(T −Tref )/z dt
0
(4.10)
T is temperature of food in ○ C, Tref is 90°C and z value is 9.84°C.
4.3.5
Effect of frequency on heating pattern
The heating pattern of the food in a microwave assisted thermal process is determined by the
resonant modes within the microwave cavity. Each resonating mode has a corresponding resonance
frequency (Sadiku, 2010). In case of multi-mode cavities small shift in frequency may result in a
different mode type and unpredictable heating patterns (Luan, Wang, Tang & Jain, 2017). MAPS
uses single mode cavities designed to operate at 915 MHz. Operating frequency may be affected
by factors such as magnetron brand, design, age and power settings. The Federal Communications
Commission (FCC) of the United States designated 915 ± 13 MHz for medical, scientific and,
industrial (MSI) uses other than telecommunications. Therefore the simulation model was used to
determine the effect of change in frequency on the heating pattern of the food for various designs
of the carriers. Frequencies in MAPS were recorded under 4, 8, 12 and 16 kW power settings
using the TM-2650 spectrum analyzer (BK Precision, California) as described in Resurreccion et
al. (2015a). Measurements for each power settings were done in 10 replicates. Simulation cases to
determine the heating pattern were performed in the range of 900-920 MHz which is in the range
of MSI allocation.
68
4.4
Results and Discussion
4.4.1
Dielectric and Thermal properties of food
Dielectric and thermal properties of mashed potato model food at 915 MHz in the temperature
range 20°C to 100°C are listed in Table 4.1. These property data were used as the inputs in the
simulation model to define the food as dielectric lossy material.
Table 4.1: Dielectric properties at 915 MHz, volumetric specific heat and conductivity of mashed
potato model food measured at temperature range 25-100°C
4.4.2
T(°C)
ε′r
ε”r
c (MJ/m3 -K)
K (W/m-K)
25
72.8 ±2.0
15.5 ± 0.9
2.77 ±0.32
0.44 ±0.04
30
74.2±2.1
16.6± 1.2
2.87 ±0.39
0.47 ±0.06
40
73.5± 2.4
18.1± 0.8
3.13 ±0.21
0.53 ±0.02
50
72.2±2.1
19.5± 0.9
3.26 ±0.10
0.56 ±0.03
60
70.5±1.7
21.4± 1.0
3.40 ±0.10
0.60 ±0.05
70
68.9±1.4
23.5± 0.5
3.53 ±0.06
0.65 ±0.03
80
67.1±0.5
25.5± 0.1
3.87 ±0.14
0.78 ±0.09
90
65.2±0.2
27.8± 0.3
3.57 ±0.12
0.69 ±0.09
100
62.3±1.0
29.3± 0.2
4.19 ±0.44
0.81 ±0.12
Influence of food carriers on electromagnetic field distribution in MAPS
Figure 4.7 (a) shows total electric field in the central plane of an empty microwave cavity. A
staggered electric field pattern with 3 distinct high intensity field zones in y direction was observed.
69
For the heating uniformity TE20 or TE 30 mode was recommended (Luan et al., 2015b). In the
MAPS system an empty cavity was designed to operate at TE30 mode. Electric field distribution in
the cavity in the presence of tray carrier with metal and UltemT M side parts is shown in the figure
4.7 (b). The side metal and ultem parts of the carrier did not affect the main operating modes.
However, the intensity of the electric field was higher when the tray carrier was present. It may be
possible that the structures made from different materials influenced the microwave scattering and
reflection within the cavity leading to higher electric field intensities.
Figures 4.8 shows the electric field distribution in the cavity for 16 oz and 10 oz tray carriers
with UltemT M cross rods (16 A and 10 A) and metal frame (16 B and 10 B ) each placed in the
center of the cavity. Black dashed lines in figure 4.8, a and c represents location of 16 oz food
package (160 mm × 125 mm) and 10 oz food package (90 mm × 135 mm), respectively. For the
16 A tray carrier four high intensity zones were observed (figure 4.8 a). These zones were equally
spaced within the food package and were away from the edges. Within one food package, electric
field intensity near the edges of the food package was low compared to middle portion of the food
package. Near the UltemT M rods high intensity electric fields were observed. UltemT M bars are
dielectric cylinders which scatter and absorb microwaves thus may be responsible for creating a
localized high intensity zone in near vicinity. The tray carrier surrounded by perforated metal plate
(16 B) resulted in two high power zones at the edges in y direction (figure 4.8 b). The electric field
in the presence of metal frame was concentrated on the edges instead of at the center. Thus the
simulations showed that in this design edges of the food packages will be heated by hot water as
well as microwaves which might lead to severe edge heating.
70
(a)
(b)
Figure 4.7: Total electric field distribution (E) in MAPS cavity a) empty b) in the presence of
carrier with side metal and UltemT M parts
71
Figure 4.8: Electric field distribution inside the cavity when tray carrier was placed in the center
(a) 16 A (b) 16 B (c) 10 A (d) 10 B; black dashed lines represent location of 16 oz food package
and 10 oz food package in sub-figure (a) and (c), respectively
For 10 oz tray carriers, in the design with UltemT M cross rods (10A) , the electric field was
concentrated near the edges of the food along y direction (figure 4.8 c ). 10 oz food packages have
smaller x dimensions than 16 oz (90 mm for 10 oz vs. 160 mm for 16 oz package ). Therefore,
in 10 A tray carrier there were seven UltemT M rods (figure 4.4) and food packages were closer to
the rods compared to the 16 oz food packages in 16 A tray carrier (figure 4.2). Close proximity
of food packages to the UltemT M rods might be responsible for the high intensity zones near the
edges in 10 oz food packages. In the second design of the 10 oz carrier (10 B), the presence of
the metal frame surrounding the food, led to electric field distribution focused in the center and
away from the vertical (y direction) edges of the tray (figure 4.8 d). Therefore it was predicted
that microwaves will heat the food in the center of the packages placed in the 10 B food carrier.
Since in the MAPS system, the cavity was filled with the hot water, the edges of the food would be
72
heated by the circulating water. Thus it was anticipated that the design of simultaneously heating
by water and microwaves will provide better heating uniformity for 10 oz food packages in 10 B
tray carrier.
4.4.3
Heating patterns using simulations and experiments
For the heating pattern simulations, electromagnetic and heat transfer equations were solved simultaneously for the assigned heating time duration. Two cavities were simulated to obtain the heating
patterns within the food packages in the central plane (x-y) immediately after the microwave heating is complete. Experiments were performed using chemical marker method, processed samples
were cut in the central layer and were analyzed using computer vision assistant method (Pandit
et al., 2007b). Figure 4.9 and 4.10 shows a comparison of experimental and simulated heating patterns for 16 oz and 10 oz food packages, respectively. For both of the designs of 10 and 16 oz tray
carriers, simulation results matched very closely with the experimental heating patterns. Chemical
marker heating patterns also validated the electric field distribution obtained in the cavity. High
electric field intensity areas correspond to the hot spots, and low intensity areas correspond to cold
spots.
For further validation, after determining locations of the hot and cold spots temperatures were
recorded at hot and cold spot locations of all four designs i.e. 16 A, 16 B, 10 A and 10 B. Temperature difference between hot and cold spot at the exit of second cavity and overall lethality were
calculated to indicate the heating uniformity. For 10 oz tray carrier designs, 10 B was better for
heating uniformity compared to 10 A which was anticipated as per simulation results. Experimental temperature profile recording showed that the temperature difference between cold and hot
spot was 5.1°C in 10 A. The difference was reduced to 1.7°C at the exit of second cavity for 10 B.
The difference in lethalities at cold spot and hot spot was 5.3 minutes in case of 10 A design. This
73
was reduced to 4.8 minutes when 10 B was used, showing overall higher uniformity when metal
frame was employed.
(a)
(b)
Figure 4.9: Heating patterns in 16 oz food packages loaded into tray carrier designs a) 16 A b) 16
B; left image is experimental heating patterns obtained by chemical marker in model food; right
image is simulation results. Areas in red and black boxes represent hot and cold spots respectively
74
(a)
(b)
Figure 4.10: Heating patterns in 10 oz food packages loaded into tray carrier designs a) 10 A b)
10 B; left image is experimental heating patterns obtained by chemical marker in model food;
right image is simulation results. Areas in red and black boxes represent hot and cold spots
respectively
75
In case of 16 oz tray carrier designs, temperature difference between cold and hot spots when
the microwave heating finished, was 12.1°C and 15.9°C for 16 A and 16 B, respectively. 16 B
in which food was surrounded by perforated metal frame resulted in higher difference in the cold
and hot spot temperatures (15.9°C). As anticipated from the simulation results, the electric field in
this design was concentrated on the edges instead of at the center. Thus edges were heated by hot
water as well as microwaves, and the cold spot at the center was heated slowly. Whereas in the
case of 16 A tray carrier, cold spot location was near the edge which got more hot water heating
than the central part, and thus temperature differences between hot and cold spot was less 12.1°C.
Temperature difference in 16 oz food packages was higher for both tray carrier designs compared
to the 10 oz food packages. Several factors might be responsible for this observation. For example,
16 oz packages were larger, which might lead to slower heat transfer to cold spots. UltemT M cross
bars were responsible for the scattering of the microwave power and distributing it evenly, less
number of cross bars in 16 A than 10 A may have resulted in higher temperature differences. Thus
it can be concluded that for 16 oz food packages, tray carrier design with UltemT M bars (16 A)
was more appropriate, however even this design led to temperature differences of 10°C, which was
still high due to the larger size of the tray. Study is in progress to optimize the design of the tray
carrier for 16 oz food packages to reduce the temperature differences further.
4.4.4
Effect of frequency on heating pattern
MAPS cavities were designed to resonate at 915 MHz. However in practical applications, it is well
known that magnetron do not release single frequency (Resurreccion et al., 2015a). Microwave
frequency of the generators in MAPS during processing were recorded under different power settings of the system. Table 4.2 shows operating peak frequency of the generator with 4, 8, 12 and
16 kW settings. Peak operating frequencies were lower than 915 MHz in tested power settings but
76
within the range of allocated frequency range by FCC (± 13 MHz). Also the operating frequency
was directly proportional to the power setting.
Table 4.2: Operating frequencies of MAPS generator for various power settings
Transmitted microwave power (kW)
Peak operating frequency (MHz)
4
904.4 ± 1.0
8
906.3 ± 0.5
12
908.7 ± 0.4
16
910.2 ± 0.2
In order to cover the lowest and highest possible operating frequency range, simulation cases
were performed for 900, 915 and 920 MHz. Figure 4.11 shows heating patterns obtained at different frequencies for all four tray carriers. Results demonstrated that the heating pattern is not
affected by the frequency shift of the microwave generator in the frequency range of 900-920
MHz for any design of the tray carrier. However product temperature is affected by the change in
frequency. As the frequency increased, hot spot areas and the temperature also increased. Similar results were obtained for microwave assisted thermal sterilization (MATS) system where food
packages were moved on a conveyor belt made from microwave transparent material (Resurreccion
et al., 2015a). Similar to MATS, the heating patterns in MAPS were independent of the frequency
variation of the generator, however the temperature of hot areas was directly proportional to the
frequency.
77
(a)
(b)
(c)
(d)
Figure 4.11: Heating patterns in the middle layer of food tray for four designs of the carrier at
900, 915 and 920 MHz for carrier designs (a) 16 A (b) 16 B (c) 10 A (d) 10 B
78
4.5
Conclusion
The durability of machinery and the uniformity of heating are of utmost importance in the industrial
scale microwave systems. A computer simulation model was used to study various designs of
food package carriers in order to improve the heating uniformity in microwave assisted thermal
pasteurization system (MAPS). Computer simulations showed that electric field pattern inside the
cavity could be modified by varying tray carrier designs. In the case of 10 oz tray carriers, best
results were obtained when a metal frame surrounding the food package was inserted in the tray
carrier. The presence of metal plate helped in homogeneous distribution of the microwave power
in the center of the tray. However in the case of 16 oz tray carriers, presence of metal frame
concentrated the power on the edges which led to a higher temperature difference in the hot and
cold spots. The model developed in this work will further be used to improve the heating uniformity
in the bigger size trays as well as in scale up of the system.
79
Chapter 5
INFLUENCE OF DIELECTRIC PROPERTIES AND THICKNESS ON ELECTROMAGNETIC HEATING OF FOODS IN 915 MHZ SINGLE MODE MICROWAVE CAVITY
5.1
Abstract
Understanding the effects of dielectric properties on the heating behavior of food is essential to
improve the heating uniformity in microwave processing systems. Calculations based on the exponential decay of electric field intensity in lossy medium provide reasonable estimations of electromagnetic power dissipation in samples thicker than few penetration depths. However, there are no
ways to quantify the role of food properties on power dissipation in samples where standing wave
patterns are formed. Here we developed a mathematical model for predicting electromagnetic
power dissipation within a rectangular dielectric slab incident by the equal intensity 915 MHz uniform plane waves from top and bottom. We proposed a dimensionless parameter, Jain-Tang (J-T)
number which is a combination of the loss factor (ε”), dielectric constant (ε′ ) and food thickness
(L). This unique number provides direct insight into the relationship between food dielectric properties, thickness, and thermal lethalities. For the validation tests, mashed potatoes, peas and rice
samples with 0-2% salt content were processed in a pilot scale microwave assisted thermal sterilization (MATS) system. In each food, the combination of dielectric properties and thickness which
gave J-T number of 1.8-2.0 at 100-121°C, provided the highest Lethalities. MATS is a commercial technology used in food industry around the world, a qualitative assessment of the combined
effect of food properties on lethalities using our model will be relevant for providing guidelines in
product formulations for MATS.
80
5.2
Introduction
Interaction of electromagnetic waves with a material is quantified by its electrical and magnetic
properties known as dielectric permittivity (ε∗ ) and magnetic susceptibility (µ∗ ) (Balanis, 2005).
For non-magnetic materials such as foods, dielectric permittivity is the primary parameter which
affects the electromagnetic energy absorption, reflection, transmission, and dissipation within the
food. Dielectric permittivity is defined as a complex number with real and imaginary parts, dielectric constant (ε′ ) and loss factor (ε”), respectively (Tang, 2015):
ε∗ = ε′ − jε” = ε0 ε′r − jε0 ε”r
(5.1)
where ε0 is dielectric permittivity of vacuum (8.85 × 10−12 F/m) and ε′r & ε”r are relative dielectric
constant and loss factor, respectively. The storage of electric energy is represented by the dielectric constant whereas thermal conversion of electrical energy is represented by the loss factor in a
dielectric material. In microwave heating, dipole rotation and electrical conduction are the dominant loss mechanisms, therefore the overall loss factor is expressed as the combination of dipolar
and conduction effects (Peng, Tang, Jiao, Bohnet & Barrett, 2013):
ε”r = ε”d + ε”σ
(5.2)
where ε”d is the relative dipole loss, and ε”σ is the relative ionic loss. Ionic contribution of the loss
factor is described by the following equation:
ε”σ =
σ
2πf ε0
(5.3)
where σ is electrical conductivity of the dielectric material and f is the frequency of electromagnetic
waves.
81
Dielectric properties of a food material are not only functions of frequency and temperature
but also depend on the food composition and combination of its ingredients. A small change to a
food product formulation may have a significant effect on dielectric constant as well as loss factor
which in turn affect the heating behavior of the food. For example, a change in an amount of salt
from 0.8% to 1.8% in mashed potatoes increases the loss factor from 38.1 to 95.2 at 121°C and
915 MHz (Guan et al., 2004). Similar effects of salt addition on loss factor has been reported
for many food products such as carrots (Peng et al., 2014), potato slice (Wang, Zhang, Mujumdar
& Jiang, 2011), meat batter (Zhang, Lyng & Brunton, 2007) and bread crumbs (Goedeken, Tong
& Virtanen, 1997). Likewise, change in an amount of water was reported to affect the dielectric
constant of food such as ham (Sipahioglu, Barringer, Taub & Prakash, 2003), eggs (Zhang et
al., 2014), mashed potatoes (Guan et al., 2004; Jain et al., 2017a) and other fruits and vegetable
(Sipahioglu & Barringer, 2003).
An understanding of the relationship between dielectric properties of foods and their microwave heating performance may help in formulating food products for improved heating efficiency and uniformity in microwave heating systems. Maxwell’s equations coupled with heat
transfer equations are used to predict the microwave heating in different scenarios for 2450 MHz
multi-mode (Datta, 1990) and 915 MHz single mode cavities (Chen et al., 2008). Usually, the real
scenarios are very complex involving food shape, thickness, rotation or translational movement
of food and temperature dependence of dielectric properties, thermal conductivity, and specific
heat. Analytical solutions to these heating problems are often difficult or impossible to obtain. Numerical techniques, e.g., finite element, finite difference, finite difference time domain are used to
calculate temperature profiles in different situation (Dibben, 2001a). The modeling procedure using these methods is very time consuming and requires specialized software and high-performance
computers. However, for practical purposes, a simple model which can predict the qualitative
82
temperature profiles based on dielectric and thermal properties may be instrumental. Ayappa and
Davis (1991), Zhang and Datta (2001), Nelson and Datta (2001), Barringer et al. (1995), Remmen
Henk, Ponne, Nijhuis, Bartels and Kerkhof (1996) solved simplified Maxwell’s equations and its
approximation Lambert’s law for thick samples at 2450 MHz. Hossan and Dutta (2012) studied
the temperature dependence of dielectric properties and had calculated the temperature profiles
within the food samples for 40 MHz, 433 MHz, 915 MHz and 2450 MHz analytically. All of these
models were developed for the multi-mode cavity systems where heating patterns change with the
dielectric properties and frequency. The primary focus of their studies was to analyze the change in
heating patterns along the thickness, the location of cold and hot spots for different sizes, shapes,
dielectric properties and locations of the food products within the cavity.
A single mode 915 MHz microwave assisted thermal sterilization (MATS) system was developed at Washington State University (Tang, 2015). In the single mode cavities, pre-packaged
food is heated simultaneously by electromagnetic waves and hot water. Microwaves enter from two
horn shaped applicators, 50% from the top horn and 50% from the bottom horn, through the circulating water to rectangular food packages. The symmetrical design of the system provides cold spot
location at the central layer inside food packages with the thickness between 16-25 mm (Resurreccion et al., 2013; Luan et al., 2015a; Jain et al., 2017a; Tang, 2015; Chen et al., 2008). Processing
of moving food packages in MATS is a complicated physical process that involves propagation
of microwaves from top and bottom horns, conversion of electrical energy into thermal energy
and heat transfer. 3-D Maxwell’s equations coupled with heat transfer equations were solved for
MATS using Quick-wave software to gain insight on electric field distribution and heating patterns
in central plane of the food packages (Resurreccion et al., 2013; Luan et al., 2015a). While the
heating pattern results obtained by computer simulations were in agreement with the experiments
performed using the chemical marker and computer vision assistant technique, our previous studies
83
have shown that the computation times were very long e.g. 42 hours per simulation run as reported
by Resurreccion et al. (2013).
In developing a MATS process schedule for a specific product, temperature measurements
at the cold spots (central layer) are performed to estimate lethality to target pathogens. Process
conditions depend on the food formulations and package geometry, in particular, food thickness.
It is desirable to develop a general understanding of how food properties, especially dielectric
properties and food thickness, influence the heating rates at the cold spot in food packages during
MATS processes. Such information would serve as general guidance for the efficient development
of process schedules. Therefore in this study, simplified Maxwell’s equations for plane waves were
solved analytically to develop general criteria as for how food properties and thickness influence
the heating rates at the cold spot inside a food package. Specific objectives of this research were
(1) To develop a simplified model for analyzing the effects of dielectric properties and thickness of
foods on 915 MHz microwave energy penetration and (2) To validate the model by experimental
measurement of lethality in mashed potatoes, peas and rice for a broad range of loss factor values
achieved by changing salt content. The model developed in this study is easy to handle and feasible
with relatively simple and less time-consuming computer software.
5.3
Mathematical models
In this study, a simplified Maxwell’s equation was solved for a uniform plane wave to obtain
electric field distribution in a rectangular food incident by 915 MHz microwaves. The power
dissipation was computed from the electric field distribution which was then used as a source term
in the heat transfer equation to obtain temperature profiles.
84
5.3.1
Governing equations
Following assumptions were applied to 3-D Maxwell’s equations to obtain the simplified model
for one-dimensional propagation in z direction in a 915 MHz single mode cavity with water immersion:
1. Electromagnetic waves were assumed to be uniform plane wave traveling from water to food
incident normally and in phase on top and bottom sides of a rectangular food (figure 5.1).
Using the coordinate system of figure 5.1, the electromagnetic waves in MATS system have
non-zero electric fields in y direction and travel in ± z direction. The magnitude of incident
electric field (E0 ) was taken as 103 V/m on each face. 103 V/m is in the range of electric
field intensities calculated for MATS system using computer simulations (Luan et al., 2016).
Figure 5.1: Schematic of a food slab immersed in water heated by 915 MHz uniform plane
waves. Electromagnetic waves are incident from top and bottom of the slab of height L. Dielectric properties i.e. dielectric constant (ε′ ) and loss factor(ε”) of water and food are denoted by
subscripts w and f, respectively
85
2. Food products were solid, homogeneous in composition and structure, they obeyed linear
material constitutive laws and had relative magnetic permeability µr = 1.
3. Only microwave power term was considered as the heat source while calculating temperature
profiles at the central layer of the food. This assumption is reasonable for the short time
microwave heating in MATS (3-5 minutes), as the microwave heating is the dominating
heating mechanism at the central layer of the food.
4. The heat diffusion rate is much slower than the heat generation, and that is why thermal
conductivity values were considered negligible. The heating rates were assumed to be a
function of volumetric heat capacity and power dissipation.
Using above assumptions, simplified time independent Maxwell’s equation for a uniform plane
wave propagating in z direction can be written as (Sadiku, 2010):
d2 E
+ γ 2E = 0
dz
(5.4)
where γ represents the propagation constant expressed as
γ = α + jβ
(5.5)
where α and β are attenuation constant and phase constant respectively. They are related to
dielectric properties and frequency as:
¿
Á ′ √
ε”r
2πf Á
Á
À εr ( 1 + ε′r − 1)
α=
c
2
¿
Á ′ √
ε”r
2πf Á
Á
À εr ( 1 + ε′r + 1)
β=
c
2
(5.6)
(5.7)
where f is frequency (Hz), c is speed of light in vacuum (3 × 108 m/s), ε′r is relative dielectric constant of food and ε”r is the relative loss factor of the food which includes dipole and conductivity
86
contribution. The boundary conditions for uniform plane wave traveling from water into the food
are given by (Sadiku, 2010):
n̂ × (E⃗w − E⃗f ) = 0
(5.8)
⃗w − H
⃗f ) = 0
n̂ × (H
(5.9)
where subscript w and f represent the water and food respectively. The solution of equation for
electric field inside the food distance z from the interface is given by:
E=
Tw/f E0
(e−γ2 z + e−γ2 (L−z) )
−γ
L
2
1 + Rw/f e
(5.10)
0≤z≤L
where E0 is the incident electric field intensity, L is food thickness, Tw/f and Rw/f are the transmission and reflection coefficient respectively in lossy medium given as (Ayappa & Davis, 1991):
Tw/f =
2ηf
ηw + ηf
(5.11)
Rw/f =
ηf − ηw
ηw + ηf
(5.12)
where ηw and ηf are complex intrinsic impedance of water and food respectively.
5.3.2
Electromagnetic power dissipation and heat transfer
The power flux for a propagating electromagnetic wave is represented by the time average Poynting
vector S over one period given by (Sadiku, 2010):
1
S⃗ = (E × H ∗ )
2
87
(5.13)
Power dissipation in a medium is given by Poynting theorem expressed in point form as
′
µ0
ε0 εr
1
E.E ∗ )
▽ .S = − ωε0 ε”r E.E ∗ + iω ( H.H ∗ +
2
2
2
(5.14)
where ω = 2πf is frequency in radians, E is electric field intensity, ε0 and µ0 is permittivity
and permeability of vacuum respectively. The theorem states that the net power flow across a
surface enclosing a volume V is sum of the power dissipated in the medium (real part) and the
stored electric and magnetic fields (imaginary part). Thus the dissipated microwave power per unit
volume is given by:
⃗
P (z) = Re(− ▽ .S)
(5.15)
= 2π f ε0 ε”r ∣E∣
(5.16)
2
hence with a knowledge of medium properties and electric field intensity the local power dissipation is calculated from equation 5.16.
A general form of energy transfer equation for a solid is given by:
▽ ⋅k ▽ T + P (z) = ρC
∂T
∂t
(5.17)
where T is temperature (°C), k (W/m-K), ρ (g/m3 )and cp (J/gK) are the medium thermal
conductivity, density and specific heat respectively. P(z) is heat source term given by equation 5.16
for the current heating case.
The solution of equation 5.17 provides transient temperature profiles in foods. As per assumption (iv), the conduction term is dropped in the calculations to give heat transfer equation
as:
P (z) = ρC
dT
dt
(5.18)
If Ti is the initial temperature (at t = 0) , temperature (○ C) after t minutes of heating is given as:
88
T=
P (z) × t
+ Ti
ρC
(5.19)
Microwave power term in the above equation was considered independent of temperature. Temperature profiles obtained from this simplified model were used to approximate the effect of change
in food formulations in relation to dielectric properties. The solutions to equations 5.16 and 5.19
were obtained using MATLAB2016.
5.4
Experimental validation
5.4.1
Sample preparation
Mashed potatoes, peas and rice were chosen for the validation of the analytical model. Salt at
different levels was used to change the values of loss factor. Mashed potato samples with 0, 0.1,
0.2, 0.5, 1 and 2% salt were prepared. Salt was added to the water followed by mixing 20% of
dried potato flakes (Oregon Potato Company, WA) in the salt solution. Peas samples were prepared
by using dried white peas (Svad, Skokie, IL). The peas were soaked overnight at room temperature
and were boiled for 60 minutes with a pea to water ratio of 1:1.5. Peas were ground and filled
inside the trays. 0, 0.1, 0.2, 0.5, 1 and 2% salt content was used for peas samples. In preparing rice
samples, medium grain rice (Nishiki, Los Angeles, CA) was used. Rice grains were pre-cooked
with rice to water ratio of 1:1.2 at 95°C for 40 minutes. 0, 0.2, 0.5, 1, 1.5 and 2 % salt was added
to the water before cooking. 0.5% D-ribose was used as a precursor of chemical marker M2 in
all the samples for heating pattern determination using computer vision assistant method (Pandit
et al., 2006).
89
5.4.2
Food properties measurement
Dielectric properties of all samples were measured using an HP 8752 C Network Analyzer and
85070B open-end coaxial dielectric probe (Agilent Technologies, Santa Clara, CA) in the microwave frequency range: 300-3000 MHz. The probe was calibrated before measuring each sample
with a short circuit (a gold-plated shorting block), an open circuit (air), and pure water at 25°C.
After calibration, a sample was filled into a cylindrical test cell. The temperature of the cell was
controlled by circulating oil from an oil bath to the sample holder. Detailed design of the system is
given by Wang et al. (2003). The measurements were carried out at temperatures of 60°C, 70°C,
80°C, 90°C, 100°C, and 121°C.
Specific heat of the samples was measured using a differential scanning calorimeter (MDSC,
Q1000, TA Instruments, New Castle, DE) as described in Sablani, Bruno, Kasapis and Symaladevi
(2009). 15-20 mg of samples were sealed in aluminum pans and were equilibrated at room temperature. The samples were heated from room temperature to 50°C at 5°C/min and equilibrated for
10 min. The samples were scanned from 50°C to 120°C at a rate of 5°C/min. Heat capacity value
was divided by the weight of the sample to obtain the specific heat values for samples. Specific
heat values were taken at 60°C which was the initial temperature of the product at the entrance of
microwave cavity. All the experiments were performed in duplicates.
5.4.3
Microwave assisted thermal sterilization (MATS) processing
Mashed potatoes, rice, and peas samples each having 6 varying levels of salt, altogether 18 recipes
were prepared. 300 grams of each sample was filled in 10 oz rectangular tray (95 (x) mm × 140
(y) mm × 25 (z) mm) and vacuum sealed with 65 mbar, 200°C and 12 seconds dwell time with a
Multivac T-200 sealer (Multivac Inc., Kansas City, MO, U.S.A.). The thickness of the food inside
90
the tray (L) was measured for all three types of foods.
A rigorous and comprehensive experimentation process was used to obtain statistically meaningful, and reliable results for MATS. First, experiments were conducted to select the appropriate
amount of D-ribose (M2 precursor) in the samples to obtain color changes in the samples which
could be detected by the computer vision assistant technique. Preliminary tests were conducted
to develop the process schedule to achieve desired lethality for shelf stable products. After preliminary tests, heating patterns and cold spot locations in each recipe was first determined. Then
temperature profiles were measured at the cold spot locations to calculate the lethality values in
consequent test runs.
Our pilot scale MATS system was able to process 48 food packages every run. Firstly, for
the heating pattern determination three separate runs were conducted to process the three food
types. In each test, 10 dummy food packages were placed at two ends of the conveyor belt, and
7-9 packages of each salt level were placed in between. Total 126 food packages (seven for each
recipe) were cut horizontally in the middle layer and images were taken using a camera set-up
as described previously in Pandit et al. (2007b). The images were analyzed by computer vision
assistant technique to obtain the heating patterns and cold spot locations. Computer vision assistant method is based on the color change of the samples after processing due to chemical marker
M2 generation in the browning reaction between D-ribose and amino acids (Pandit et al., 2006).
Software converts the whole image into red, green and blue colors, depending upon the intensity
of heat treatment received. Areas which receives more thermal treatment are converted to red and
least are turned to blue. Medium heat treatment areas are converted to green (Pandit et al., 2007b).
Samples with different salt levels were analyzed together at the same color scale by the software
to compare the heating patterns for each kind of food.
For temperature measurements in the pre-determined cold spot locations, cumulatively six
91
runs (48 packages per run) on our MATS system were conducted using same process schedule. In
one run, samples with three different salt levels for the same food were processed. For example,
in one test, mashed potatoes samples with 0, 0.1 and 0.2% salts were treated, and samples with
0.5, 1 and 2% salt levels were treated in another test. For one recipe, temperature measurement
was performed in triplicates. Prior to each run, mobile metallic Ellab temperature sensors (Ellab
Inc, Hilleroed, Denmark) were placed at the cold spot locations in the trays, as described in Luan
et al. (2015b). The food trays with temperature sensors were separated by the trays filled with same
food without sensors to avoid any interference in the temperature measurements. Temperature data
were recorded at every 2 seconds, and the F0 value was calculated using the following equation
(Holdsworth, 1997):
F0 = ∫
t
10(T −121.1)/10 dt
(5.20)
0
where T is the temperature (°C) at the cold spot and t is the time in minutes.
The MATS system used in this study had four sections, i.e., preheating, microwave heating,
holding and cooling. Each section had a circulating water heated to a pre-set temperature controlled
by a plate heat exchanger. The food samples were placed on a mesh conveyor belt and loaded to
the preheating section. After preheating, the samples were moved through the microwave heating
section then the holding section and finally to the cooling section. System description is given in
detail by Resurreccion et al. (2013). The water temperature in preheating, heating, holding and
cooling sections were set at 61°C, 124°C, 124°C and 23°C, respectively. The power setting for the
four microwave heating cavities in the MATS system were 6, 5, 3.0 and 3.2 kW based on previous
tests to reach the desired thermal lethality. Food was preheated for 35 minutes in the system, moved
through the microwave heating section over 4.5 minutes. The food trays then moved through the
holding section for 4.7 minutes and cooled down in the cooling section for 5 minutes and unloaded.
92
5.5
Results and Discussion
5.5.1
Analytical results
Electromagnetic power dissipation along the food thickness
This section presents the analysis of the electromagnetic power dissipation along the microwave
propagation direction (z) as a function of food thickness (L) and dielectric properties. The equal
intensity (1V/mm) in phase 915 MHz microwaves was incident on top, and bottom surfaces of
rectangular food packages placed in water at 124°C. The relative dielectric constant and relative
loss factor of water at this temperature and 915 MHz is 56 and 3, respectively (Tang, 2015).
A typical thickness for single meal trays or pouches used in MATS system is in the range
of 16-25 mm. Thus the effect of food thickness on the power dissipation per unit volume P (z)
were calculated for food thickness (L) = 15 mm , 18 mm, 22 mm, 24 mm, 26 mm and 30 mm using
equation 5.10 and 5.16. The calculations were made for dielectric constant (ε′r ) values of 40, 50, 60
and 70 and loss factor (ε”r ) values of 5, 30, 100 and 150. These dielectric properties were chosen
based on the values obtained at processing temperatures for various food products with different
formulations (Wang et al., 2003).
Figure 5.2 shows the power dissipation profiles in foods with different thickness as influenced
by dielectric constants at loss factor (ε”r ) = 30. The loss factor value was chosen based on the
experience for optimum penetration of 915 MHz microwaves in MATS (Wang et al., 2003). As
the food thickness increases, the power penetration to the central layer of the food decreases from
1.7 kW /m3 for L = 15 mm to 0.95 kW /m3 for L = 30 mm when ε′r = 40. For the foods with
the thickness 15-24 mm (figure 5.2 a-d), a single broad peak is observed around the central layer.
However as the food thickness increases above 24 mm (figure 5.2, e & f), multiple resonances,
93
i.e., multiple peaks and dips were observed which may result in alternate hot and cold spots along
the food thickness. For food with thickness 30 mm (figure 5.2 f), power dissipation at the surface
is almost same as that of the central layer, whereas, for all other thicknesses, power dissipation is
more at the central layer compared to at the surface (figure 5.2 a-e).
For a given thickness, food dielectric constant doesn’t affect the overall number of resonances
of the power distribution. In the packages with comparatively shallow depths (L = 15 mm, 18
mm and 22 mm) overall power dissipation decreases as the dielectric constant value of the food
increases (figure 5.2 a-c). For L = 24 and 26 mm (figure 5.2 d & e), power dissipation follows a
similar trend in central region (0.2 < z/L < 0.8). Near the surface a maximum power dissipation
is obtained when food had ε′r = 70. For L = 30 mm (figure 5.2 f), power dissipation at the surface
and the central region (region of maxima) increases with increasing dielectric constant of the food,
but it decreases in the areas close to minima.
Figure 5.3 shows power dissipation distribution along the microwave propagating direction
(z) for foods with loss factors 5, 30, 100 and 150 in packages of various thickness and dielectric
constant (ε′r ) = 50. For foods with loss factor values of 5 and 30, the sum of the forward moving and
backward moving electromagnetic waves within the samples leads to maximum power dissipation
at the central layer for all thicknesses (L = 15-30 mm, figure 5.3 a-f) . For loss factors 100 and
150, most of the microwave power was absorbed in the surface for samples with thicknesses L =
18 mm to 30 mm (figure 5.3 b-f). For 15 mm thick sample, surface layer absorbed more power
than central layer only at ε”r = 150 (figure 5.3 a). For L = 15 mm and 18 mm (figure 5.3, a & b),
when loss factor was 150, the power declined rapidly into the foods reaching a minimum at the
central layer. But the dissipated power in the center was still higher in the foods with loss factor
= 150 compared to foods with loss factor = 5 where most of the microwave power was absorbed
around the central area.
94
Our results showed that food with thickness between 15-24 mm and a range of food dielectric properties (ε′r = 40-70, ε”r = 30-70) is suited for MATS processing; where circulating water
heats the food surface,and microwaves provide the maximum dissipation at the center of the food
packages, resulting in the relatively uniform heating profiles. Higher loss factor values such as
εr ” > 100,(equivalent to 2% salt in mashed potatoes (Guan et al., 2004)) would lead to most of
the power absorption at the surface, which in turn would result in severe non-uniform heating and
therefore not recommended for MATS processing.
95
96
loss factor (ε”) = 30 and dielectric constants (ε′ ) of 40 (−−), 50 ( ), 60 (⋯) and 70 (-●-)
Figure 5.2: Influence of food thickness (L) on power distribution along the wave propagation direction (z) in a food with a
97
dielectric constant (ε′ ) = 50 and dielectric loss factors (ε”) of 5 (−−), 30 (
), 100 (⋯) and 150 (-●-)
Figure 5.3: Influence of food thickness (L) on power distribution along the wave propagation direction (z) in a food with a
Electromagnetic power dissipation at the central layer
This section analyzes the effect of a change in dielectric properties of food products on the power
absorption profile at the central layer (L/2) which is a cold spot location in food packages during
MATS processing (Luan et al., 2015b; Resurreccion et al., 2013; Tang, 2015). Figure 5.4 shows
the volumetric power dissipation at z=L/2 as a function of loss factor for L = 15 mm, 20 mm and
25 mm thick food and dielectric constants (ε′r ) = 40, 50, 60 and 70.
Figure 5.4: Influence of dielectric properties on power dissipation profiles at the central layer of
15 mm, 20 mm and 25 mm thick food
The microwave power dissipation in the central layer first increased with the increase in loss
factor of the food. After reaching a maximum value, the power dissipation decreased. This trend
was same for all values of dielectric constants and food thickness. Equation 5.16 shows that microwave power absorption is directly proportional to the loss factor and square of electric field
98
intensity. As discussed in the previous section, the electric field intensity at the central layer of
food depends on the penetration ability of the microwaves. The penetration depth is inversely proportional to food loss factor, and less microwaves penetrate to the central layer inside food with
higher values of loss factor. Therefore, after reaching a maximum power dissipation, further increase in the loss factor of food would contribute to more dissipation but it would be limited to the
surface of the food and central layer would be heated less.
The effect of dielectric constant is complex, however, but not as drastic as loss factor. For low
loss factor up-to 20, microwave power dissipation decreases as the dielectric constant increases.
This relationship is similar to that observed in low loss dielectric materials such as water where the
material is relatively transparent to microwaves (Tang, 2015). In those cases, low values of dielectric constant provide higher penetration depths (Komarov & Tang, 2004; Tang, 2015). However,
for high loss factor foods, power dissipation values increase with the dielectric constant.
It is desirable to obtain high microwave power dissipation at the central layer, i.e., cold spot
locations to increase the heating efficiency and uniformity of food packages processed in MATS.
The value of loss factor which provides the maximum power absorption at the central layer varies
with the product thickness as well as the dielectric constant of the foods (figure 5.4). For a given
product thickness, the value of loss factor at which the maximum power dissipation (Pmax ) occurs
increases with increasing dielectric constant. Whereas for a given dielectric constant, the value
of loss factor decreases with increasing thickness to obtain maximum power dissipation (Pmax ).
For example in product with thickness (L) of 15 mm, and dielectric constant (ε′r ) = 40, Pmax is
obtained when loss factor (ε”r ) is 49. For same thickness (L = 15 mm), if dielectric constant is
70, the loss factor value to obtain maximum dissipation changed to 59. For L = 20 mm and ε′r
= 40, loss factor should be 34, and at ε′r = 70, the loss factor should be 43 to obtain maximum
dissipation. Similarly, for L = 25 mm, at ε′r = 40 , loss factor should be 26 and at ε′r = 70, the loss
99
factor should be 34 for maximum power dissipation. Based on the above observations, it appears
to be a complicated process to estimate the optimum set of food properties and thickness to achieve
the maximum dissipation at the central layer in MATS. Thus, to estimate the overall influence of
these factors (thickness, dielectric constant and loss factor) on the microwave power absorption,
we proposed a dimensionless number as:
ωLε”
2πf Lε”
2πε”L
√
= √√
= √√
c ∣ε∗ ∣ c
ε′2 + ε”2
ε′2 + ε”2 λair
(5.21)
where c is the speed of microwave propagation in the air (3×108 m/s) and λair is the wavelength
of microwaves in free space. In this number, the loss factor (ε”) incorporates the microwave
power absorption, dielectric permittivity term (∣ε∗ ∣) incorporates the transmission and reflection of
microwaves, and thickness (L) of the food includes the penetration effect. Figure 5.5 shows the
plot of power absorption in the central layer vs. this number. The power dissipation in the central
layer of the food package reaches a maximum, corresponding to the highest heating rates when the
dimensionless number is in between 1.8-1.9 for all thickness and dielectric constants. This value
provides maximum heating rates as a function of dielectric properties and thickness, in the central
layer of a rectangular dielectric slab incident by in phase and equal intensity 915 MHz microwaves
from top and bottom. We refer this unique combination of parameters as Jain-Tang (J-T) number.
100
Figure 5.5: Microwave power dissipation at the central layer of a package vs J-T number for
foods with dielectric constant (ε′ )= 40 (−−), 50 (- ⋅ -), 60 (⋯) and 70 ( ) and package thickness
L = 15 mm, 20 mm and 25 mm
Temperature profiles
The absorbed electromagnetic power obtained from simplified Maxwell’s equation (5.16) was used
as a heat source in the energy equation (5.19) for calculating temperature distribution within the
food. Specific heat cp and density ρ of a substance are important factors for calculating the heating
rates and temperature achieved. A material with a lower value of volumetric specific heat (ρ × cP )
requires less amount of energy for a unit change in temperature. Thus even if power dissipation
within two types of food is equal, one food might get heated faster than the other, depending upon
the volumetric specific heat values.
101
Figure 5.6: Temperature as a function of J-T number and volumetric specific heat at the central layer of 18 mm thick food heated by 915 MHz microwaves for 3 minutes when incident by
1V/mm electric field on both faces for food with with dielectric constant (ε′r )= 40 (−−), 50 (- ⋅ -),
60 (⋯) and 70 ( )
Figure 5.6 shows the temperature profiles calculated at z = L/2 of 18 mm thick foods with
different volumetric specific heat values when the food was exposed to 915 MHz microwaves for
3 minutes. Electric field intensity of 1V/mm was incident on top and bottom of the food package.
The temperature profiles are similar to the power dissipation patterns; however temperature values
depends upon the volumetric specific heat. For the same value of the J-T number and dielectric
constant, there is a difference of 10-20°C when volumetric specific heat changes from 4.5 to 3.5
MJ/m3○ C. Lethality is a cumulative effect of time and temperature. Thus even small temperature
differences lead to more pronounced changes in F0 value. An advantage of this temperature approximation is that it will aid in the assessment of the effect of a change in product formulation on
102
the heating performance of food packages within a MATS system.
5.5.2
Food properties and analytical temperature distribution in mashed potatoes, peas and rice
For MATS processing, 300 grams of mashed potatoes (ρ = 1.1 × 103 kg/m3 ), peas (ρ = 1.3 ×
103 kg/m3 ) and rice (ρ = 0.96 × 103 kg/m3 ) were vacuum sealed at 65 millibar. The rectangular
slabs obtained after the vacuum provided a thickness of L = 23 mm for mashed potatoes, 18 mm
for peas and 25 mm for rice in a 140 mm long and 95 mm wide tray. Table 5.1 lists the specific
heat values for peas, mashed potatoes, and rice, respectively for different salt levels. Tables 5.2,
5.3 and 5.4 show the dielectric constant, loss factor and J-T number at 915 MHz in the temperature
range of 60°C-121°C.
Loss factor of food increased with increasing salt content for all three foods. The increase in
loss factor of the samples with increasing salt content was due to the increase in ionic contribution
of the loss factor due to dissolved ions of sodium chloride. The loss factor also increased with the
temperature, except for rice at 0% salt level for which loss factor does not change with temperature.
However, salt did not influence the dielectric constant significantly. These results are in agreement
with the previous finding in different foods (Guan et al., 2004; Peng et al., 2014; Wang et al., 2011;
Zhang et al., 2007; Jain et al., 2017a). The salt content also did not change the specific heat values
of the samples.
The one-dimensional plane wave model developed in this study was used to compare the temperatures profiles of mashed potatoes, peas and rice using the experimentally measured physical
and dielectric properties of the food samples as inputs. The food was exposed to 1V/mm 915 MHz
microwaves for 4.5 minutes from the top and bottom faces. The volumetric specific heat of the
food sample was calculated by multiplying its density to the average specific heat of all salt levels.
It was 4.7M J/m3 for peas, 3.8M J/m3 for mashed potatoes and 3 M J/m3 for rice. Figure 5.7
103
shows analytical calculations for temperature achieved in mashed potatoes, peas and rice vs. J-T
number (0-6) corresponding to a wide range of loss factors (ε”r = 0-300). Even though rice had the
highest thickness (25 mm) compared to mashed potatoes (23 mm) and peas (18 mm), the temperature achieved by supplying the same amount of power was more for rice for the same value of J-T
number. The higher temperature values in rice samples were due to the lowest value of volumetric
specific heat.
Table 5.1: Specific heat of mashed potatoes, peas and rice with 0-2% salt content at 60°C
Sample
Salt level (%)
cp (J/g ○ C)
Mashed potatoes
0.0
0.1
0.2
0.5
1.0
2.0
3.46 ± 0.00
3.56 ± 0.08
3.30 ± 0.02
3.46 ± 0.17
3.52 ± 0.01
3.55 ± 0.07
Peas
0.0
0.1
0.2
0.5
1.0
2.0
3.50 ± 0.06
3.46 ± 0.03
3.65 ± 0.04
3.75 ± 0.02
3.61 ± 0.09
3.67 ± 0.02
Rice
0.0
0.2
0.5
1.0
1.5
2.0
3.04 ± 0.01
3.26 ± 0.00
3.17 ± 0.00
3.22 ± 0.02
3.25 ± 0.05
3.23 ± 0.07
104
Table 5.2: Dielectric properties (dielectric constant ε′r and loss factor ε”r ) and J-T number of
mashed potatoes with 0 %, 0.1%, 0.2%, 0.5%, 1% and 2% salt content at 915 MHz in the temperature range 60°C-121°C and L = 23 mm
Salt content (%)
Temperature (○ C)
0
60
70
80
90
100
110
121
0.1
60
70
80
90
100
110
121
0.2
60
70
80
90
100
110
121
0.5
60
70
80
90
100
110
121
1
60
70
80
90
100
110
121
2
60
70
80
90
100
110
121
ε′r
ε”r
√
2πf ε”L/c ∣ε∗∣
59.1 ± 0.3
57.4 ± 0.1
56.3 ± 0.1
55.7 ± 0.1
54.8 ± 0.4
54.1 ± 0.4
54.6 ± 1.1
23.1 ± 1.7
25.5 ± 1.8
27.4 ± 1.7
29.7 ± 1.7
32.4 ± 1.5
35.4 ± 1.5
40.8 ± 1.4
1.3 ± 0.1
1.4 ± 0.1
1.5 ± 0.1
1.6 ± 0.1
1.8 ± 0.1
1.9 ± 0.1
2.1 ± 0.1
60.6 ± 0.2
58.7 ± 0.0
57.9 ± 0.1
56.9 ± 0.1
55.9 ± 0.4
55.4 ± 0.4
54.3 ± 1.2
19.1 ± 0.1
20.8 ± 0.1
22.2 ± 0.2
24.1 ± 0.8
25.4 ± 1.1
26.9 ± 1.9
29.3 ± 2.0
59.9 ± 1.1
58.2 ± 1.2
57.1 ± 1.6
55.8 ± 1.8
54.8 ± 1.8
54.2 ± 1.7
54.6 ± 1.6
26.9 ± 2.6
30.2 ± 2.5
32.8 ± 2.4
37.1 ± 0.9
40.5 ± 0.8
43.9 ± 0.7
50.5 ± 0.1
60.2 ± 0.4
58.4 ± 0.5
57.4 ± 0.4
56.8 ± 0.4
55.7 ± 0.6
55.1 ± 1.0
54.8 ± 1.8
38.7 ± 4.7
43.5 ± 4.3
47.1 ± 3.5
51.2 ± 3.2
56.1 ± 2.7
60.1 ± 2.2
66.7 ± 0.8
60.3 ± 1.7
58.7 ± 1.9
57.8 ± 2.3
56.9 ± 2.5
56.5 ± 2.5
56.1 ± 2.7
56.7 ± 2.8
54.4 ± 0.1
61.4 ± 0.3
67.2 ± 0.1
74.4 ± 0.0
82.1 ± 0.8
90.3 ± 1.2
101.2 ± 0.5
62.6 ± 1.0
61.5 ± 0.6
60.7 ± 0.7
59.9 ± 0.8
59.3 ± 1.1
58.8 ± 1.3
58.5 ± 1.4
86.3 ± 5.5
100.1 ± 4.0
113.6 ± 6.1
124.9 ± 6.0
138.4 ± 5.4
153.4 ± 5.1
167.6 ± 4.6
105
1.1 ± 0.0
1.2 ± 0.0
1.2 ± 0.0
1.3 ± 0.0
1.4 ± 0.1
1.5 ± 0.1
1.6 ± 0.1
1.5 ± 0.2
1.6 ± 0.2
1.8 ± 0.1
2.0 ± 0.1
2.2 ± 0.1
2.3 ± 0.1
2.6 ± 0.0
2.0 ± 0.2
2.2 ± 0.2
2.4 ± 0.1
2.6 ± 0.1
2.8 ± 0.1
2.9 ± 0.1
3.2 ± 0.0
2.7 ± 0.0
2.9 ± 0.0
3.2 ± 0.0
3.4 ± 0.0
3.6 ± 0.0
3.9 ± 0.0
4.2 ± 0.0
3.7 ± 0.2
4.1 ± 0.1
4.4 ± 0.2
4.7 ± 0.1
5.0 ± 0.1
5.3 ± 0.1
5.5 ± 0.1
Table 5.3: Dielectric properties (dielectric constant ε′r and loss factor ε”r ) and J-T number of
peas with 0%, 0.1%, 0.2%, 0.5%, 1% and 2% salt content at 915 MHz in the temperature range
60°C-121°C and L = 18 mm
Salt content (%)
Temperature (○ C)
0
60
70
80
90
100
110
121
0.1
60
70
80
90
100
110
121
0.2
60
70
80
90
100
110
121
0.5
60
70
80
90
100
110
121
1
60
70
80
90
100
110
121
2
60
70
80
90
100
110
121
ε′r
ε”r
√
2πf ε”L/c ∣ε∗∣
52.7 ± 3.5
51.9 ± 3.4
51.1 ± 3.0
50.6 ± 2.5
50.1 ± 2.2
49.6 ± 1.9
49.2 ± 1.3
18.3 ± 2.8
19.8 ± 2.7
21.1 ± 2.7
22.6 ± 3.2
24.8 ± 3.2
26.6 ± 2.8
28.6 ± 3.2
0.8 ± 0.1
0.9 ± 0.1
1.0 ± 0.1
1.0 ± 0.1
1.1 ± 0.1
1.2 ± 0.1
1.3 ± 0.1
55.0 ± 3.7
53.8 ± 3.6
52.8 ± 3.4
52.4 ± 2.9
51.6 ± 2.7
50.4 ± 3.0
49.4 ± 3.3
14.2 ± 2.0
15.6 ± 2.0
16.6 ± 2.1
17.8 ± 2.0
19.2 ± 1.9
20.4 ± 2.0
21.2 ± 2.3
55.0 ± 2.0
54.2 ± 1.6
52.9 ± 1.5
51.7 ± 0.9
51.2 ± 1.0
50.9 ± 0.5
50.2 ± 0.5
22.9 ± 4.6
25.3 ± 5.0
27.2 ± 5.1
30.2 ± 5.2
32.0 ± 5.2
34.4 ± 5.4
37.2 ± 4.4
57.2 ± 2.9
56.0 ± 2.2
55.1 ± 1.7
54.5 ± 1.4
53.7 ± 1.1
52.9 ± 0.8
51.8 ± 0.4
32.3 ± 0.3
37.6 ± 2.0
40.5 ± 2.5
42.6 ± 2.4
47.3 ± 2.7
51.1 ± 2.7
55.7 ± 4.5
57.3 ± 1.9
56.5 ± 1.2
56.0 ± 1.1
55.6 ± 0.9
54.9 ± 0.6
54.3 ± 0.4
53.8 ± 0.3
51.4 ± 4.5
58.1 ± 6.7
62.2 ± 7.2
66.6 ± 7.8
73.4 ± 7.1
79.6 ± 6.8
85.3 ± 7.4
56.6 ± 4.5
55.8 ± 4.1
55.4 ± 3.9
54.9 ± 3.4
54.6 ± 2.9
54.0 ± 2.9
53.9 ± 2.3
83.3 ± 4.8
92.0 ± 7.1
98.6 ± 8.9
107.1 ± 9.3
117.3 ± 8.2
125.8 ± 7.9
122.9 ± 7.5
106
0.6 ± 0.1
0.7 ± 0.1
0.8 ± 0.1
0.8 ± 0.1
0.9 ± 0.1
0.9 ± 0.1
1.0 ± 0.1
1.0 ± 0.2
1.1 ± 0.2
1.2 ± 0.2
1.3 ± 0.2
1.4 ± 0.2
1.5 ± 0.2
1.6 ± 0.1
1.4 ± 0.0
1.6 ± 0.1
1.7 ± 0.1
1.8 ± 0.1
1.9 ± 0.1
2.1 ± 0.1
2.2 ± 0.1
2.0 ± 0.1
2.2 ± 0.2
2.3 ± 0.2
2.5 ± 0.2
2.6 ± 0.2
2.8 ± 0.1
2.9 ± 0.1
2.7 ± 0.1
2.9 ± 0.1
3.1 ± 0.2
3.3 ± 0.2
3.5 ± 0.1
3.6 ± 0.1
3.8 ± 0.1
Table 5.4: Dielectric properties (dielectric constant ε′r and loss factor ε”r ) and J.T. number of
rice with 0%, 0.2%, 0.5%, 1%, 1.5% and 2.0% salt content at 915 MHz in the temperature range
60°C-121°C and L = 25 mm
Salt content (%)
Temperature (○ C)
0
60
70
80
90
100
110
121
0.2
60
70
80
90
100
110
121
0.5
60
70
80
90
100
110
121
1.0
60
70
80
90
100
110
121
1.5
60
70
80
90
100
110
121
2.0
60
70
80
90
100
110
121
ε′r
ε”r
√
2πf ε”L/c ∣ε∗∣
54.7 ± 0.1
53.4 ± 0.1
52.1 ± 0.1
50.9 ± 0.2
49.7 ± 0.1
48.8 ± 0.3
48.1 ± 0.1
7.7 ± 0.2
8.2 ± 0.3
8.9 ± 0.5
9.5 ± 0.7
10.4 ± 1.0
10.8 ± 0.8
11.3 ± 1.0
0.5 ± 0.1
0.6 ± 0.0
0.6 ± 0.1
0.7 ± 0.1
0.7 ± 0.1
0.8 ± 0.1
0.8 ± 0.1
55.4 ± 1.1
53.6 ± 1.5
52.4 ± 1.4
51.5 ± 1.6
50.3 ± 1.6
49.3 ± 1.1
48.7 ± 0.8
20.9 ± 1.9
23.1 ± 1.8
24.6 ± 1.3
26.4 ± 1.1
28.4 ± 0.3
30.1 ± 0.5
30.6 ± 0.5
1.3 ± 0.1
1.4 ± 0.1
1.5 ± 0.1
1.7 ± 0.1
1.8 ± 0.0
1.9 ± 0.0
1.9 ± 0.0
60.6 ± 0.2
58.7 ± 0.0
57.9 ± 0.1
56.7 ± 0.1
55.1 ± 0.7
54.6 ± 0.4
54.2 ± 0.2
6.6 ± 0.8
6.5 ± 0.5
6.3 ± 0.1
6.3 ± 0.0
6.4 ± 0.3
6.5 ± 0.3
7.0 ± 0.1
58.1 ± 0.4
56.8 ± 0.1
55.4 ± 0.1
54.1 ± 0.2
52.7 ± 0.1
51.7 ± 0.2
51.0 ± 0.1
13.9 ± 1.0
15.0 ± 1.3
16.4 ± 1.1
17.7 ± 0.9
18.8 ± 0.8
20.0 ± 0.7
20.3 ± 0.6
56.9 ± 1.5
55.4 ± 0.7
54.4 ± 0.5
53.0 ± 0.1
51.5 ± 0.4
49.8 ± 0.8
48.3 ± 1.6
34.1 ± 0.1
37.9 ± 0.3
41.8 ± 0.1
47.1 ± 0.0
50.3 ± 0.8
52.3 ± 1.2
51.7 ± 0.5
61.3 ± 1.0
60.4 ± 1.1
59.4 ± 1.5
58.2 ± 1.9
57.2 ± 2.1
56.3 ± 2.6
55.1 ± 3.3
55.8 ± 1.0
61.8 ± 0.2
68.9 ± 0.4
76.1 ± 1.1
81.8 ± 1.8
87.4 ± 1.6
91.0 ± 1.3
107
0.4 ± 0.1
0.4 ± 0.0
0.4 ± 0.0
0.4 ± 0.0
0.4 ± 0.0
0.4 ± 0.0
0.5 ± 0.0
0.8 ± 0.1
0.9 ± 0.1
1.0 ± 0.1
1.1 ± 0.0
1.2 ± 0.0
1.3 ± 0.0
1.3 ± 0.0
2.0 ± 0.1
2.2 ± 0.1
2.4 ± 0.1
2.7 ± 0.0
2.8 ± 0.0
2.9 ± 0.0
2.9 ± 0.0
2.9 ± 0.0
3.2 ± 0.0
3.4 ± 0.0
3.7 ± 0.0
3.9 ± 0.0
4.1 ± 0.0
4.2 ± 0.0
Figure 5.7: Temperature at the central layer of mashed potatoes (⋯), peas ( ) and rice (−−) calculated analytically using plane wave model for 4.5 minutes of microwave heating by 915 MHz
(E0 = 1V/mm on each face)
Peas had the highest volumetric specific heat, yet for the J-T number < 2.2 (in the low loss
factor range), heating in peas was more than in mashed potatoes. That is because of the lower
thickness (18 mm for peas vs. 23 mm for mashed potatoes) and lower values of dielectric constants (52 for peas vs. 56 for mashed potatoes) which lead to more microwaves reaching central
layer in the pea packages. For J-T numbers > 2.2 (higher loss factors), the heating was more
in mashed potatoes compared to peas, this reversal was observed previously in figure 5.4 where
power dissipation decreases with decrease in dielectric constant for high loss factor range. Thus
less power dissipation in the central layer of peas combined with high volumetric specific heat
resulted in less heating of peas compared to mashed potatoes for large values of J-T numbers.
108
5.5.3
Experimental results
Heating patterns
Figure 5.8 shows heating patterns in the central layers of mashed potatoes, peas and rice samples
obtained using computer vision assistant technique after MATS processing. Since the background
color of food matrices and reaction rates for chemical marker formation are different among the
three types of food samples, the color change of samples can not be used to compare the heat
treatment intensity between the various food types. However, for each type of food, the sample
colors with different salt levels were analyzed on the same scale. Among the mashed potatoes
samples, 0.1% salt samples had the highest color change. Among the peas samples, the sample
with 0.5% salt indicated the most intense heat treatment. For the rice samples, the sample with
1% salt had the most severe heat treatment. The heating patterns of the samples with different salt
content were similar with two symmetrical hot areas. Similar heating patterns were obtained in the
past for processing with MATS using whey protein gels of the various dielectric properties (Tang,
2015; Luan et al., 2015b) and have been confirmed by computer modeling (Resurreccion et al.,
2015b). However, the rice sample at 0 % salt was heated more at the edges, and there was less
heating at the center. Rice at this salt level had a low loss factor value of 7. The sample was almost
transparent to the microwaves; thus there was much small microwave power absorption, and the
sample was heated mainly by the circulating hot water. Table 5.5 shows cold spot locations (x-y
plane) in all the samples.
109
(a)
(b)
(c)
Figure 5.8: Experimental heating patterns in the central layer of (a) mashed potatoes, (b) peas,
and (c) rice samples as determined by chemical marker M2. Numbers on the top represent the salt
levels from 0-2%. Red color represents more heated areas, blue and green represent lowest and
medium heat treatments, respectively
110
Table 5.5: Cold spot locations at the central layer of mashed potatoes, peas and rice samples with
0-2% salt content; x and y represent the horizontal and vertical distance, respectively from the
center of the tray
Sample
Salt content (%)
X (mm)
Y (mm)
Mashed potatoes
0.0
0.1
0.2
0.5
1.0
2.0
27.3 ± 1.7
27.7 ± 0.8
30.4 ± 0.1
19.9 ± 2.0
-26.2 ± 0.7
19.0 ± 1.8
1.2 ± 1.0
1.4 ± 1.4
1.5 ± 1.0
-49.9 ± 0.3
-53.0 ± 1.1
52.3 ± 0.4
Peas
0.0
0.1
0.2
0.5
1.0
2.0
12.8 ± 1.8
17.1 ± 0.6
28.2 ± 1.4
26.4 ± 0.6
-26.7 ± 0.6
-23.7 ± 2.1
55.6 ± 2.0
53.4 ± 1.2
54.8 ± 0.2
56.3 ± 1.0
-46.6 ± 1.3
-45.1 ± 2.3
Rice
0.0
0.2
0.5
1.0
1.5
2.0
0.0 ± 0.0
25.1 ± 1.5
30.1 ± 0.2
31.7 ± 2.9
31.4 ± 2.0
34.4 ± 2.3
0.0 ± 0.0
1.4 ± 1.1
1.5 ± 1.1
-2.1 ± 2.6
-22.6 ± 4.7
-34.8 ± 5.3
111
Lethality measurement
Figure 5.9 shows the lethality values at the cold spots of food samples after MATS processing
vs salt content . These data confirm the heating pattern results obtained using chemical marker
technique. 0.1% salt level among mashed potatoes samples, 0.5% salt among peas and 1% salt
among rice samples provided the highest lethalities.
25
Mashed potatoes
Peas
Rice
1.5
2
Lethality (minutes)
20
15
10
5
0
0
0.5
1
2.5
Salt content (%)
Figure 5.9: Lethality (F0 ) in minutes measured experimentally as a function of salt for mashed
potatoes (▲), peas (●) and rice (∎)
Dielectric properties of a food sample are dependent on temperature; therefore dielectric constants and loss factors of food samples were measured from the initial temperature of food in MATS
112
processing (60°C) to sterilization temperature (121°C). Corresponding J-T numbers are given in
table 5.2, 5.3 and 5.4 for mashed potatoes (L = 23 mm) , peas (L = 18 mm) and rice (L = 25 mm),
respectively. The samples which had J-T numbers between 1.8-2.1 at temperature 100-121°C (0.1
% for mashed potatoes, 0.5 % for peas and 1 % for rice) were heated the most. Foods with a
lower amount of salt levels had J-T number values < 1.6 at all temperatures (60-121.1°C). These
food samples accumulated less lethality. Foods with a higher amount of salt (> 0.1 % for mashed
potatoes, > 0.5 % for peas and > 1% for rice) had a J-T number value of > 1.8 at 60-121°C. Except
for mashed potatoes with 0.2% salt where J-T number reached 1.8 at 80 °C. These samples which
had J-T numbers values greater than 1.8 in the temperature (100-121°C) were heated less. To explain this observation lets take the pea sample with 1 % salt as an example. This sample had J-T
number = 2.01-2.21 at 60-70°C. This implies that pea with 1 % salt absorbed maximum power at
60-70°C just at the start of the microwave heating, which raised the temperature further. However,
at higher temperatures, microwave power absorption in the same product was reduced, leading to
lower heating rates and lethalities. Lethality starts to add up when the cold spot temperatures reach
greater than 100 °C. Therefore the pea sample with 1 % salt accumulated lesser lethality compared
to samples which absorbed maximum power in the temperature range 100-121°C or samples which
had J-T number 1.8-2 at 100-121°C. Thus a value of dielectric loss factor and J-T number calculated by taking an average of its values at 100, 110 and 121°C was used to compare the heating
behavior of food samples.
Figure 5.10 summarized experimental results on the influence of loss factor on lethalities at
the cold spots in mashed potato, peas, and rice samples. The graph indicates that for peas (L = 18
mm), maximum lethality was achieved when loss factor was 51. Whereas for mashed potatoes (L
= 23 mm), highest lethality was obtained at loss factor of 36, and for rice (L = 25 mm) loss factor
was 30. These experimental results agree with the analytical results (figure 5.4 ) which showed
113
that with an increase in the thickness, loss factor values decreases to obtain the maximum power
dissipation.
Mashed potatoes
25
Peas
Rice
Lethality (minutes)
20
15
10
5
0
0
50
100
150
200
Loss factor (εr")
Figure 5.10: Lethality (F0 ) in minutes measured experimentally as a function of loss factor for
mashed potatoes (▲), peas (●) and rice (∎)
Figure 5.11 shows experimental results of lethality values as a function of the J-T number. The
results indicate that maximum heating is achieved at a J-T number between 1.9-2.0 for the three
different foods. These experimental data matches closely with the calculations (figure 5.4, 5.6 and
5.7 ), which showed that irrespective of the food type, J-T number for the maximum absorption is
constant. Rice samples accumulated the more lethality compared to peas and mashed potatoes for
114
the same value of the J-T number and the shift in heating trends among mashed potatoes and peas
was also observed in the experimental results similar to analytical results (figure5.7 and 5.11). The
close agreement between experimental data and analytical calculations confirms that the model
developed in this research works well for predicting microwave power dissipation at the central
layer of food packages processed in MATS.
Table 5.6 summarizes the effects of dielectric properties, thickness and volumetric specific
heat of the food on the heating efficiency of food products. Based on the results of this work, the
table provides recommendations on values of these parameters to obtain highest power dissipation
at the central layer of a rectangular food package during MATS processing.
Figure 5.11: Lethality (F0 ) in minutes measured experimentally for mashed potatoes (▲), peas
(●) and rice (∎) as a function of J-T number
115
116
Volumetric specific heat (ρcp )
Food thickness (L)
Dielectric Loss Factor (”)
Dielectric Constant (ε′ )
Parameter
• Lower heating rates
• Low power dissipation in the central
layer and high surface heating
• Number of resonances increases with
alternate hot and cold spots
• Less penetration
• More dissipation on surface
• More central heating by increasing
up-to 50-70; further increase will
cause less heating at central layer
• Lower power absorption at the central
layer for low loss factor foods
• Higher power absorption at the central
layer for high loss factor foods
Effects of increasing
Volumetric specific heat can be modified by changing
density or specific heat of the final product via modification of ingredients. For example increasing amount of oil
and fats reduce volumetric specific heat.
Inside out microwave heating and surface heating by circulating hot water will provide the most uniform heating
for L = 15-25 mm. Depending upon the density, thickness
of food in packages can be modified by controlling weight
of the food filled in the packages.
ε”r = 35-60 at 121°C for food thickness 15-25 mm will
provide the highest power absorption at the middle layer
and thus uniform heating. Loss factor values can be
modified by changing salt content.
ε′r = 55-58 at 121°C will provide the most uniform heating. Since hot circulating water has ε′r = 56-58, it will
minimize the reflection at the water-food interface. Value
of dielectric constant can be increased via addition of
water and reduction in fat or oil content and vice-versa.
Recommendations for MATS
Table 5.6: Summary of results: effect of change in dielectric constant, loss factor, thickness and volumetric specific heat on
food products heated in microwave assisted thermal sterilization (MATS)
5.6
Conclusion
In this paper, influence of dielectric properties, thickness and volumetric specific heat on the heating rate of the food product during 915 MHz microwave processing were evaluated using analytical
mathematical models. We proposed and validated a dimensionless parameter called J-T number
to assess relative heating rates of different food formulations and food packages under the same
conditions in MATS processes. Validation experiments on peas, mashed potatoes, and rice were
conducted in pilot scale MATS system . The process developers can use this dimensionless number
to select the process parameters for new formulations in food packages. The model can be used to
develop process for multi-compartment trays in which two or more types of foods are processed
simultaneously in the same MATS system; the J-T number will be useful to asses which food
would heat more than the other and select appropriate formulations or shielding to achieve similar
lethality in different compartments. Although the calculations and experiments were conducted for
microwave assisted sterilization conditions, the same model can also be used to guide the selection
of process conditions for microwave assisted thermal pasteurization (MAPS) where J-T number of
foods at 70-90°C will be relevant.
117
Chapter 6
ANALYSIS OF TWO COMPARTMENT TRAYS HEATING PATTERNS IN MICROWAVE ASSISTED THERMAL PASTEURIZATION SYSTEM
(MAPS) USING J-T NUMBER
6.1
Abstract
This paper analyzed the heating patterns in 10 oz multi-compartment food packages processed in
microwave assisted thermal pasteurization (MAPS). Mashed potato model food with 0%, 0.6% and
1.2% salt levels were used to represent three types of foods with varying loss factors. Dielectric
properties, and J-T number was calculated for all samples at 915 MHz and 60-100°C. Two compartments of the food trays were filled with different types of food samples and processed in pilot
scale MAPS system. Heating patterns of the samples were detected by a chemical-marker based
computer vision method. Results showed that food with 0.6% salt was always the most heated and
food with 1.2% salt was the least heated irrespective of the size of the compartment.
6.2
Introduction
Development of 915 MHz single mode microwave assisted pasteurization system (MAPS) at Washington State University has opened a market potential for in-package pasteurized meals that have
fresh-like taste, richer texture and higher nutrient values compared to foods processed by conventional thermal processing methods (Tang, 2015). MAPS combine volumetric microwave heating
with hot water surface heating to reduce the overall processing time and yield high quality ready
to eat meals (RTE) (Resurreccion et al., 2013). Current RTE meals in markets are available in
variety of new and creative packages, meals in prepackaged multicompartment trays particularly
118
appeal to consumers. But differences in thermal and dielectric properties of those meals pose challenges in design of thermal processes. When a multi-compartment tray carrying two or more types
of foods is processed using same microwave processing conditions, foods with different thermal,
physical and dielectric properties may have different heating rates, which in turn, lead to large
differences in lethalities. MAPS technology provides a solution to this processing challenge by
introducing novel metal carrier designs to transport multi-compartment food packages inside microwave cavities. The carriers have flexibility to attach a metal pattern sheet over and under part
of the multi-compartment trays to achieve similar heating rates among two different food compartments (Tang & Liu, 2017). It is also possible to fill the two types of foods with different initial
temperatures to achieve similar final temperature.
To implement shielding or adjust heating rates in foods on the MAPS tray carriers, it is important to understand the heating behaviour of different foods in microwave heating. It is required
to estimate which food heats faster than the other, so that appropriate compartment can be shielded.
The thickness of food packages and dielectric properties of the food, i.e., dielectric constant and
loss factor, are the main factors which affect the microwave transmission, reflection and dissipation
within a food product during microwave processing (Datta, 1990). Increase in temperature within
food also depend on the volumetric specific heat values of each food component. In this study
a simple case was considered where loss factor of a food was changed, while keeping all other
factors constant to analyze the change in heating patterns within a 10 oz two-compartment trays.
The objective of this study was to determine the relative heating rates among foods having different dielectric properties when they are processed together in multi-compartment trays. A mashed
potato model food was chosen with 0, 0.6 and 1.2% salt levels to represent three different foods.
Changing salt content was used to modify the loss factor as described in Wang et al. (2003), Jain
et al. (2017a), Zhang et al. (2007). Penetration of microwaves depends strongly on the loss factor
119
of foods which affects the heating rates of foods (Guan et al., 2004). Effect of difference in loss
factor on the heating patterns of two compartment trays was studied using chemical marker technique (Pandit et al., 2006). Color change of the sample due to browning of fructose was used to
evaluate the heating patterns of the food in computer vision assistant method (Pandit et al., 2007b).
6.3
Materials and Methods
6.3.1
Food preparation
For heating pattern determination in food processed in MAPS, model foods are cut in the central layer and image analysis is performed using computer vision assistant technique (Pandit et al.,
2007b). To locate the cold spots and hot spots accurately using image analysis, the model food system must change color at pasteurization temperatures and have opaque matrix (Jain et al., 2017a).
It was also desirable that the model food has firm texture so that it can be cut precisely at the central
layer. Thus to fulfill these requirements, a mashed potato-gel was developed as a model food in
this study. Fructose browning in alkaline conditions was used as chemical marker which changed
color in pasteurization conditions as described in Jain et al. (2017a). As carrier of the marker precursors, mashed potato mixed with gellan gel was used. The presence of mashed potatoes imparted
opaqueness and gellan gel provided firm texture which was easy to cut at the central layer.
Mashed potato-gel model food samples were prepared with 0, 0.6 and 1.2% added salt. 1%
low acyl gellan polymer (Kelcogel, CP kelco, US) was added to DI water at room temperature.
The polymer mixture was heated to 90°C, and 4% dried potato flakes (Oregon potato company,
WA) along with selected amount of salt was added to the hot mixture. Heating was stopped when
the mixture became homogeneous solution and the solution was allowed to cool down to 70°C.
0.4% liquid titanium dioxide and 1.5% fructose were added to the solution at 70°C and was cooled
120
further to 65°C. 0.1% sodium hydroxide and 0.3% calcium chloride was added and mixed further
for one minute. Detailed discussion of gellan gel formation and texture can be found in Tang,
Lelievre, Tung and Zeng (1994) Tang, Tung and Zeng (1996) Tang, Tung and Zeng (1997). In this
work, two-compartment trays with 10 oz overall capacity were used for the processing (figure 6.1).
Figure 6.1: Mashed potato model food filled in 10 oz two-compartment food packages
Large compartment of the tray is referred as A, it was 85 × 90 × 30 mm in dimensions. Small
compartment is referred as B , it was 46 × 90 × 30 mm in dimensions. 200 g solution was poured
in large compartment and 100 g sample was poured in small compartment and were kept in refrigerator for 1-2 hours. Thickness of the food inside the tray was 18 mm in both compartments. The
food trays were then vacuum packed (sealing conditions: 100 mbar, 200°C, 4s dwell time) for the
processing.
6.3.2
Food properties
HP 8752 C Network Analyzer and 85070B Open-End Coaxial Dielectric Probe (Agilent Technologies, Santa Clara, CA) was used for the dielectric properties measurement of the model food
samples. Probe was calibrated using air, gold block and pure water at 25°C. Food was cut into
cylindrical shape sample and was filled into the test cell. Measurements were performed in the microwave frequency range: 300-3000 MHz at temperatures of 60°C, 70°C, 80°C, 90°C, and 100°C
121
as described in Zhang et al. (2014), Zhang et al. (2015).
In MAPS, microwaves were incident on food from top and bottom faces, thus a 1-D model was
developed by Jain, Tang, Pedrow, Tang and Sablani (2017b) considering equal intensity in phase
plane wave incidence from top and bottom of the food package. The model was developed by
solving Maxwell’s equations and incorporating internal reflections within a rectangular food slab
and a dimensionless parameter (Jain-Tang number) was proposed to estimate the power dissipation
at the central layer. In this work measured dielectric properties of model food samples were used
to calculate Jain-Tang (J-T) number using the formula (Jain et al., 2017b):
2πε”L
√√
ε′2 + ε”2 λair
(6.1)
where λair is wavelength in air, ε′ is dielectric constant, ε” is loss factor and L is food thickness.
For a food sample, combination of dielectric properties and thickness which provide J-T number
1.8 was the most heated at the central layer of a rectangular slab (Jain et al., 2017b). If J-T
number of a sample deviates from 1.8, less power was absorbed and lower lethalities were obtained.
Mathematically, it can be expressed as,
P (z) ∝
1
∣1.8 − JTf ood ∣
(6.2)
where P(z) is the dissipated power at the central layer of the food and JTf ood is J-T number for a
sample. Heating rate of a sample at the central layer, where microwave heating is the dominant
mechanism, is directly proportional to the microwave power dissipation and inversely proportional
to the volumetric specific heat:
dT P (z)
=
dt
ρC
(6.3)
dT
1
∝
dt
ρC × (1.8 − JTf ood )
(6.4)
Therefore,
122
Thus heating rates of two food samples with different volumetric specific heat and different dielectric properties can be compared by calculating ρC × (1.8 − JTf ood ). Lower the value of this parameter, higher will be the heating rate and vice-versa.
Double needle probe KD2 (Decagon Devices Inc, Pullman, WA) was used to measure the
volumetric specific heat of the samples at 60°C. A Dual needle (SH-1), 30 mm long, 1.28 mm
diameter probe with 6 mm spacing between needles was used. The KD2 probe was carefully
inserted into the food sample inside the test cell. The temperature of the sample was controlled by
circulating oil from an oil bath.
6.3.3
Microwave assisted thermal pasteurization (MAPS) processing
A pilot scale MAPS system used in this study had four sections viz, preheating, microwave heating,
holding and cooling (figure 6.2). The microwave heating section consisted of two rectangular
cavities connected to a 915 MHz microwave generator. The details of the design of the single mode
cavities for the heating section is described by Tang (2015). The process schedule in this work was
selected to achieve a 6 log reduction of nonproteolytic Clostridium botulinum type E spores (90°C,
10 minutes) (Peng et al., 2017b). The preheating water, circulating water in the cavity, holding
section and cooling temperature were set at 61°C, 93°C, 93°C, and 23°C, respectively. Sealed
food packages were placed on a designed tray carrier (figure 6.1 b) and moved inside the cavity
on a set of wheels. Microwave processing time of the food was controlled by speed of the carrier
movement. Food was pre-heated for 30 minutes, heated in the microwave section with a residence
time of 2.8 minutes, and then the food trays were moved to the holding section for 5 minutes. The
samples were cooled down in the cooling section for 5 minutes and unloaded.
123
Preheating section
Holding section
Microwave heating section
Cavity 1
50% mw power
50% mw power
Cooling section
Cavity 2
50% mw power
50% mw power
Figure 6.2: Schematic diagram of pilot scale 915 MHz single mode microwave assisted thermal
pasteurization system
Figure 6.3: Horizontal top view of the tray carrier loaded with vacuum sealed 10 oz twocompartment food packages
To analyze the effect of change in heating rates on heating patterns within multi-compartment
trays, five different sets of samples were treated in MAPS (figure 6.4): (a) Food with 0% salt was
filled in both compartments of the trays, (b) 0% salt sample was filled in the small compartment,
124
and 0.6% in the large compartment, (c) 0.6% salt food was filled in the small compartment, and
0% in the large compartment, (d) 0% salt food was filled in the small compartment and 1.2% in
the large compartment, (e) 1.2% salt food was filled in the small compartment and 0% in the large
compartment. A metal carrier was used to transport 6 food packages per run though the MAPS.
To determine the influence of package direction on heating patterns, food packages were placed in
two different orientation for each case. 3 trays were placed in such a way that small compartment
was in front and in 3 trays large compartment was in front (figure 6.3).
125
(a)
(b)
(c)
(d)
(e)
Figure 6.4: Experiment design for MAPS processing, 200 gram of food was filled in compartment A and 100 gram of food was filled in compartment B: Foods with 0%, 0.6%, and 1.2% salt
were filled in five different orientations and were processed in MAPS using same processing
schedule
126
6.3.4
Heating pattern determination by computer vision assistant
For heating pattern determination, MAPS processed model food was cut horizontally in the central layer, and the images were taken using a camera set-up described previously by Pandit et al.
(2007b). The analysis of the images was done by computer vision assistant technique as described
in Pandit et al. (2007b). The software converted the most heated parts of the processed model
food in red color (hot regions) and least heated to blue color (cold spot). Areas which received the
medium amount of thermal energy were converted to green color. Based on the lowest and highest
color values within the samples, exact location of cold and hot spot was determined.
6.3.5
Temperature profile
To record the temperature, PICO-VACQ 1Tc mobile metallic temperature sensors manufactured
by TMI-Orion (Castelnau-le-Lez, France) were used. 10 oz food trays were filled with 300 g of
mashed potato model food, the and temperature sensors were embedded in the samples so that the
tips were located at the cold spot. Food packages were sealed with lid films, sealing conditions
were 100 mbar, 200○ C for 4 seconds dwell time with a vacuum sealer (Multivac T-200, Multivac
Inc., Kansas City, MO, U.S.A). Samples were processed at 7 KW power, and tray speed of 13.5
mm/s. This speed provided 2 minutes of microwave heating. The trays were then treated by hot
water in the holding section for 10 minutes at 90°C. Finally, all trays were cooled in the cooling
section at 23°C.
127
6.4
Results and Discussion
6.4.1
Food properties
Dielectric constants and loss factors of three model foods at 915 MHz at 60, 70, 80, 90 and 100°C
are listed in table 6.1. Dielectric constant of food samples decreased with temperature at all levels
of salt. However salt did not have much effect on dielectric constant values. Loss factor values
increased with the salt content as well as temperature. This is attributed to the increase in ionic
contribution in the loss factor due to sodium and chloride ions. Similar results were obtained in past
where salt was used to modify the loss factors values in various food products (Zhang et al., 2015;
Zhang et al., 2007; Guan et al., 2004; Jain et al., 2017a). J-T number of sample was calculated with
L = 18 mm. J-T number value increased with the increase in salt content as well as temperature.
Samples with 0.6% salt had J-T number between 1.8-2.4 at 60-90°C. J-T number was less than 1.2
at all temperature for sample with 0% salt and it was greater than 2.5 for samples with 1.2% salt.
Volumetric specific heat (ρcp ) of sample with 0% salt was 3.4 ± 0.1 M J/m3 K, for the sample
with 0.6% salt was 3.5 ± 0.1 M J/m3 K and for the sample with 1.2% salt was 4.0 ± 0.2 M J/m3 K
6.4.2
Heating pattern results
Figure 6.5 shows heating patterns of food packages for cases: (a) Food with 0% salt was filled
in both compartments of the trays, (b) 0% salt sample was filled in the small compartment, and
0.6% in the large compartment, (c) 0.6% salt food was filled in the small compartment, and 0%
in the large compartment, (d) 0% salt food was filled in the small compartment and 1.2% in the
large compartment, (e) 1.2% salt food was filled in the small compartment and 0% in the large
compartment.
128
The six samples of each individual case were analyzed for the color change on the same scale.
Location of hot and cold areas, in all six trays from one case were the same. Same heating patterns
in each case showed that orientation of the compartments (small in front or large in front) did
not affect the location of cold and hot spots. When samples were analyzed on the same scale,
variation in color from one tray to another represented the difference in amount of heat received
by the trays. For each case, the change in color of all 6 trays was very close to each other, except
for case 5 where the large compartment of first two trays was more red compared to rest of the
trays. Small variation in the colors of processed samples from one package to another, showed
that 6 food packages processed simultaneously on one tray carrier received similar heat intensity
treatments. From each case, package with the minimum color change (or most green/blue) was
selected to analyze for the cold spot location.
129
Table 6.1: Dielectric properties (dielectric constant ε’ and loss factor ε”), and J-T number of
mashed potato-gel model food with L = 18 mm, at 915 MHz in temperature range 60°C-100°C
Salt (%)
ε′
ε”
J-T number
60
70.5 ± 0.2
21.1 ± 0.3
0.9 ± 0.0
70
68.8 ± 0.0
22.8 ± 0.1
0.9 ± 0.3
80
66.9 ± 0.1
24.9 ± 0.2
1.0 ± 0.0
90
64.9 ± 0.1
27.1 ± 0.2
1.1 ± 0.0
100
62.1 ± 0.1
28.5 ± 0.0
1.2 ± 0.0
60
69.9 ± 0.1
48.7 ± 0.1
1.8 ± 0.0
70
68.1 ± 0.0
53.5 ± 0.0
2.0 ± 0.1
80
66.1 ± 0.1
58.8 ± 0.2
2.2 ± 0.0
90
64.0 ± 0.2
65.3 ± 0.1
2.4 ± 0.1
100
62.4 ± 0.1
71.0 ± 0.0
2.5 ± 0.0
60
69.3 ± 0.9
71.5 ± 3.2
2.5 ± 0.1
70
67.7 ± 0.8
79.6 ± 3.1
2.7 ± 0.1
80
66.4 ± 0.7
88.7 ± 3.6
2.9 ± 0.1
90
67.3 ± 1.9
97.7 ± 2.9
3.1 ± 0.0
100
63.0 ± 0.8
106.8 ± 2.52
3.3 ± 0.1
Temperature
(○ C)
0
0.6
1.2
130
(a)
(b)
(c)
(d)
(e)
Figure 6.5: Heating patterns of trays obtained by chemical marker technique (a) case 1: 0% salt
food in both compartments, (b) case 2: 0% salt in large compartment and 0.6%in small compartment, (c) case 3: 0.6% salt in Large compartment and 0 %in small compartment, (d) case
4: 0% salt in large compartment and 1.2% in small compartment, (e) case 5: 1.2% salt in large
compartment and 0% in small compartment
131
(a)
(b)
(c)
(d)
(e)
Figure 6.6: Cold spot locations in 10 oz two-compartment trays filled with different type of foods
for (a) case 1: 0% salt food in both compartments, (b) case 2: 0% salt in large compartment
and 0.6%in small compartment, (c) case 3: 0.6% salt in Large compartment and 0 %in small
compartment, (d) case 4: 0% salt in large compartment and 1.2% in small compartment, (e) case
5: 1.2% salt in large compartment and 0% in small compartment
Figure 6.6 shows the heating patterns of one food package per case analyzed individually to
obtain the cold spot location. When same food (0% salt) was kept in both compartments (figure
132
6.6 a ), small compartment was heated slightly more and cold spot location was in the large compartment. Since, with different orientation of the multi-compartment tray the location of the cold
spot was always in the large compartment for this case, the faster heating of small compartment
may be attributed to the faster heat transfer rates of hot water to the small compartment. For case 2
(figure 6.6b) where sample with 0% salt was kept in the large compartment, and 0.6% salt sample
was in small compartment, cold spot was also located in the large compartment. However in case 3
(figure 6.6 c, 0% in small compartment and 0.6 % in large compartment) cold spot location shifted
to small compartment. This showed that food with 0.6% salt content was heated more than the
food with 0% salt and, therefore, in case 2 cold spot location did not shift since faster heating food
was kept in the faster heating compartment. However, when the food with faster heating rate was
kept in the large compartment where heat transfer was slow, the cold spot location shifted to small
compartment. In cases 4 and 5, the cold spot location was always in the compartment with food
1.2% salt. This implies that the food with 1.2% salt content was heated slower than the food with
0 % salt.
6.4.3
Temperature profile
Heating pattern experiments showed that cold spot location shifted between compartments of multcompartment trays with the change in food type. The cold spot was always located in the food
which was heated slowly irrespective of whether it was filled in small compartment or large compartment of the food tray. Therefore temperature measurements were performed in single compartment tray filled with one food to compare the heating rates to confirm the results of heating
pattern experiments. Temperature profiles obtained at the cold spot location is shown in figure 6.7.
133
Figure 6.7: Temperature profiles at the cold spot within the single compartment 10 oz tray filled
with 0% (- ⋅ -), 0.6% ( ) and 1.2% (−−) salt model food samples
Food with 0.6% salt content was heated most, followed by food with 0.0% salt. However,
for 1.2%, maximum temperature in the central layer of the tray was 70°C during the microwave
heating which was much less than the other two food samples. This result matches with the heating
pattern results in chemical marker where compartment with 1.2% salt was always the least heated
followed by 0% salt sample.
In this study, for mashed potato model food, J-T number with 0% salt was 1.1, for 0.6% salt,
it was 2.3, and 3.1 for 1.2% salt sample. Based on equation 6.2, deviation of the J-T number
of the food sample from 1.8 estimates the efficiency of power absorption. For the sample with
134
0% salt, the deviation was +0.7, for the sample with 0.6% salt, the deviation was +0.5, and for
1.2% salt sample, it was −1.3. This showed that the model food sample with 1.2% salt absorbed
the lowest power and model food sample with 0.6% salt absorbed the highest power among three
formulations. According to equation 6.3 heating rates is a combination of volumetric specific heat
and power absorption. For model food with 0% salt ρC × (1.8 − JTf ood ) was 2.38, for 0.6 it was
1.75, and for 1.2% salt sample it was 5.2. High value of ρC × (1.8 − JTf ood ) implied lower heating
rates according to equation 6.4. Food with 1.2% salt had the highest value of ρC × (1.8 − JTf ood ).
Therefore, it absorbed less power compared to other two samples and was the least heated.
6.5
Conclusion
In this paper, effect of salt content on relative heating rates and heating patterns in multi-compartment
trays during microwave assisted thermal pasteurization process was evaluated using chemical
marker. Mashed potato model food with 0%, 0.6% and 1.2% salt content were heated in 10 oz
two compartment trays. Experiments showed that food with 0.6% was heated the most and 1.2%
was heated the least. It was shown that the location of hot and cold spots shifted within the compartments of the tray depending upon the salt content of the food samples. Although in this study
a simple model food was studied where only dielectric loss factor was variable, it helped in estimating relative heating rates among components having different salt content in multi-compartment
trays, and enabled us to find out the locations of hot and cold spots. J-T number combined with
volumetric specific heat measurements, accurately estimated that food with 1.2% salt will be heated
least followed by 0% and 0.6% salt sample was the most heated.
135
Chapter 7
CONCLUSION & FUTURE WORK
Microwave thermal sterilization and pasteurization (MATS and MAPS) technology developed at
Washington State University got approval by the United States Food and Drug Administration
(FDA) in 2009 and the United States Department of Agriculture Food Safety and Inspection Service (USDA, FSIS) non objection certificate in 2012. Currently MATS and MATS are in the
commercialization stage with pilot scale units installed in U.S.A., Australia and India. This dissertation developed tools to analyze heating patterns and heating rates of foods in MAPS and MATS
systems. Work presented here draws motivation from industrial need to understand the effects of
change in food thickness, food formulations and, novel way of food transportation in the cavity on
heating efficiency and uniformity during the processing.
Stainless steel food carriers were designed for the MAPS system, which are durable and
corrosion resistant. This dissertation developed a model food based on fructose degradation under
alkaline conditions which changed color at pasteurization temperature. The model food was used
as a tool to study the heating patterns of foods processed using different designs of food carriers in
MAPS. Dielectric properties of the model food was adjusted by changing amounts of salt and sugar
to match with the wide range of food products. A computer simulation model was then developed
and validated to analyze the electric field distribution within the MAPS cavity with the presence
of metal food carriers. Heating patterns and heating uniformity of 10 oz and 16 oz food packages
using computer simulations and experiments showed predictable heating patterns.
To compute relative heating rates of foods in complex microwave heating process is a complicated and time consuming task. In this research we developed a 1-D analytical model for 915
MHz incidence on top and bottom phase of the rectangular food package. The model was used for
136
qualitative comparison of heating rates of different foods in single as well as multi-compartment
food packages. Based on the previous experience of food processing schedules, the model will
help in minimizing the number of tests required to optimize food formulations and processing
schedules. Calculations based on J-T number were applied to compare heating rates in multicompartment food trays where two different types of foods were processed together.
7.1
Contributions of this dissertation
A mashed potato model food was developed to study heating patterns of food processed in MAPS
which is compatible with existing computer vision assistant technique to determine hot and cold
spot locations. Development of the model food based on chemical marker technique was first
and most important task, as there is no other alternative available till now to obtain the cold spot
locations in microwave processing. Accurate determination of heating patterns is critical for food
safety as well as food quality. Model food was also required to validate the computer simulation
results.
A computer simulation model was built in Quickwave software to analyze the electric field
patterns in the MAPS system in the presence of metal food carriers. Different food package sizes
require varying designs of food carriers. The carriers differ in number and size of metal parts, polyethermidie parts and their arrangement, which affect the heating uniformity. A validated computer
simulation model will aid in the concept designing of these carriers, saving time and operating cost
in the preliminary testing.
Till now, there is no standard, when it comes to food formulation with optimum combination of dielectric, thermal and physical properties to obtain the efficient power absorption during
137
microwave processing. As a result, many preliminary experiments needs to be conducted to optimize the formulations and determine the processing schedule. Quickwave models developed for
MATS and MAPS estimating the effects via computer simulations require high computing time
and resources thus they were not practical in the real commercialized settings. In this research, a
dimensionless number (Jain-Tang) was proposed which is a combination of dielectric properties
and food thickness and provides direct insight into the lethality as affected by food formulations.
When the number is equal to 1.8 maximum microwave power dissipation and hence highest lethalities were obtained and as it deviates (± 1.8) lethality values were lower.
7.2
Future Works
This work gives us validated tools, and a framework of steps that may be followed to estimate the
effects of change in food properties, thickness and food carrier designs on heating patterns and
heating rates in MATS and MAPS processing.
1. The industrial scale design of food carriers in MAPS/MATS is still in rapid evolution, and
various size of single and multi-compartment food packages are under study to obtain uniform heating patterns. The design of the carriers will undergo many changes as per the
requirements of food processing industry. There is a need to optimize the carrier designs for
large size such as 16 oz or 32 oz food packages for military ration, which could be a further
extension of this work.
2. The new tray carrier designs developed for MAPS and MATS have flexibility to attach metal
frame on top and bottom to provide shielding to the food packages. The different patterns
of the shields can be studied using computer simulation model to obtain the uniform heating
patterns in single as well as multi-compartment food trays.
138
3. In chapter 6, we presented a preliminary exploration to find if heating rates within the microwave heating can be compared using simple analytical expressions when thickness of the
package is kept constant, without the need of solving equations. The validation was performed in multi-compartment trays with changing salt content in the model food. Further
experiments are required to analyze the heating rates with changing dielectric as well as
thermal properties of the foods.
4. In real scenario most of the food packages are non-homogeneous, 1-D analytical model
developed in this study can be explored to compare of heating rates in heterogeneous food
components processed together.
139
Appendix A
PLANE WAVE INCIDENCE FROM TOP AND BOTTOM OF A RECTANGULAR
DIELECTRIC SLAB
This section presents details about the analytical solution procedure, using boundary-value approach, for determining electric field intensity inside a dielectric slab (food) surrounded by water
in a 915 MHz single mode cavity as illustrated in figure 4.10. Initially, two plane waves at the
interfaces between water and top food surface (region 1 and region 2) and water and bottom food
surface (region 2 and region 3) were incident. Both incident waves (Ei aˆy ) were considered to be
of same intensity E0 and in phase (fig.A.1).
Figure A.1: Plane wave normally incident on two interfaces of food-water
At the interfaces wave is partially reflected and partially transmitted to the food. As the
multiple reflection process takes place between the three regions, there would be infinite number
of waves travelling in +z and -z direction within each region. Steady state expressions for the
electric field in each region is obtained by summation of all the fields resulting from the reflection
140
and transmission.
Fields in region 1 (water)
In this region at a steady state, there is an incident wave propagating in +z direction and an reflected
wave propagating in -z direction:
Ê1 (z) = Ê0 e−γ0 z aˆy + Êw1 eγ0 z aˆy
(A.1)
where Ê0 is amplitude of incident wave, and Êw1 is amplitude of reflected wave. Subscript represents region of water (w1).
Fields in region 2 (food)
In this region, there would be a wave propagating in positive z direction and a wave propagating
in negative z direction. Following the same steps as above, the steady state expression of electric
field in region 2 can be given as:
= Êf 1 e−γf z aˆy + Êf 2 eγf z aˆy
(A.2)
where subscript f1 is for amplitude of waves propagating in food in +z direction and f2 represents
waves travelling in food in -z direction.
Fields in region 3 (water)
From figure A.1, it is clear that we considered two side incidence of waves therefore in this region
we have incident wave travelling in -z direction, and reflected waves travelling in +z direction.
141
Since we considered equal intensity (E0 ) incidence at both interfaces, steady state electric field in
region 3 can be given as:
= Ê0 eγw (z−L) aˆy + Êw2 e−γw (z−L) aˆy
(A.3)
After obtaining expressions for electric fields, the unknown amplitude of waves can be obtained by solving the equations using known boundary conditions. Since both the medium are
dielectric, the tangential components of electric fields at the interface are continuous. Mathematically, the boundary conditions for uniform plane wave traveling from water into the food are given
by (Sadiku, 2010):
n̂ × (E⃗w − E⃗f ) = 0
(A.4)
⃗w − H
⃗f ) = 0
n̂ × (H
(A.5)
So by applying continuity of tangential components of electric field at z = 0, we obtain:
Ê0 + Êw1 = Êf 1 + Êf 2
(A.6)
For continuity of tangential magnetic field:
−
Êf 1 Êf 2
Ê0 Êw1
+
=−
+
ηw
ηw
ηf
ηf
(A.7)
where ηw and ηf are complex intrinsic impedance of water and food respectively. Combining
equations A.6 and A.7 gives:
Ê0 − (Êf 1 + Êf 2 − Ê0 ) Êf 1 Êf 2
=
−
ηw
ηf
ηf
(A.8)
The transmission and reflection coefficient, respectively in lossy medium given as (Ayappa &
Davis, 1991):
Tw/f =
2ηf
ηw + ηf
142
(A.9)
Rw/f =
ηf − ηw
ηw + ηf
(A.10)
Substituting expressions from equations A.9 and A.10 into equation A.8 and with some rearrangement, equation A.8 reduces to :
Ê0 Tw/f = Êf 1 + Rw/f Êf 2
(A.11)
Similarly after applying boundary conditions for tangential components of electric and magnetic fields at second interface between food and water at z = L, following expressions are obtained:
Êf 1 eγf L + Êf 2 eγf L = Ê0 + Êw2
(A.12)
Êf 1 eγf L Êf 2 eγf L Ê0 Êw2
+
=
−
ηf
ηf
ηw
ηw
(A.13)
E0 Tw/f = Ef 1 e−γf L Rw/f + Ef 2 eγf L
(A.14)
−
After solving equations A.11 and A.14 simultaneously we obtain:
E0 Tw/f =
Tw/f E0 − Ef 2 eγf L
+ Ef 2 Rw/f
Rw/f e−γf L
(A.15)
With some rearrangement following expressions for amplitude of waves propagating in positive
direction and negative z direction (Ef 1 and Ef 2 ) are obtained:
Ef 1 =
Tw/f E0
Rw/f e−γf L + 1
(A.16)
Ef 2 =
Tw/f E0 e−γf L
Rw/f e−γf L + 1
(A.17)
143
Since for the present case we are just interested in the fields in food region, it can be obtained by
substituting unknown amplitudes (Ef 1 and Ef 2 ) from equations A.17 and A.16 in equation A.2:
Ef ood = Ef 1 e−γf z + Ef 2 eγf z =
Ef ood =
Tw/f E0 e−γf z
Tw/f E0 e−γf L eγf z
+
Rw/f e−γf L + 1
Rw/f e−γf L + 1
Tw/f E0
(e−γf z + e−γf (L−z) )
Rw/f e−γf L + 1
(A.18)
(A.19)
Similarly, following same procedure to find unknown amplitudes, fields in region 1 and region 3
can be obtained.
144
Appendix B
ANALYSIS OF ELECTRIC FIELD DISTRIBUTION IN TANG-CAGE
Tang-cage are novel tray carriers designed to improve heating uniformity of food packages in
MAPS systems. A metal frame is attached on the top and bottom of food package carriers which
modify electric field distribution within the food packages. In this study, different dimensions and
orientation of metal frame was studied to analyze the effect on electric field distribution for 10
oz food packages. One cavity was simulated in Quick-wave software and the tray carriers were
placed in the center of the cavity. Cases shown in figure B.1 were simulated using a validated
computer simulation model developed in chapter 4 of this dissertation. a) 10 oz tray without Tangcage shield, b) a single vertical metal bar with width wv of 2.75 mm, 5.5 mm, 11 mm and 22 mm,
c) a single horizontal metal bar with width wh of 2.75 mm, 5.5 mm, 11 mm and 22 mm, d) two
vertical bars with width of 5.5 mm each and distance between them gv of 2.75 mm, 5.5 mm, 11
mm and 22 mm, and e) two horizontal bars with width of 5.5 mm each and distance between them
gh of 11 mm, 22 mm, 33 mm, 44 mm and 55 mm. These width and gaps were chosen as fraction
or multiple of wavelength of 915 MHz (44 mm) in water at 90°C. Simulation results showed that
presence of vertical metal bars lowers the electric field intensity drastically below the locations of
the bars. Whereas presence of horizontal bars do not block the microwaves completely and scatters
the electric field. Horizontal bars with width less than 5.5 mm do not have any significant effect on
the electric field intensity. Whereas bars with width greater than 5.5 mm scatter the electric field
in the vicinity and reduce the electric field intensity. Thus for cases, where complete shielding is
required, vertical bars can be chosen. However in cases where partial blocking or distribution of
electric field is desirable horizontal bars of width greater than 5 mm can be chosen. These results
for single compartment 10 oz trays showed that two horizontal bars each of thickness 5.5 mm and
145
with gap 55 mm between them distributed the electric field most uniformly in x-y plane.
(a)
(b)
Figure B.1: a) Nomenclature for placement of shield according to moving directions of trays,
blue bar represent metal. Metal bars were placed on top and bottom of the tray carriers in same
orientations, b) Simulation cases, wv and wh are width of the metal bars. gv and gh are the gap
between two bars. Subscript v and h represents vertical and horizontal orientations respectively
Figure B.2: Electric field pattern without Tang-Cage
146
Figure B.3: Electric field pattern when single vertical bar with different width (wv ) were placed
on top and bottom of the tray carriers
Figure B.4: Electric field pattern when single horizontal bar with different widths (wh ) were
placed on top and bottom of the tray carriers
147
Figure B.5: Electric field pattern when two vertical bars with different gap in between them (gv )
were placed on top and bottom of the tray carriers
Figure B.6: Electric field pattern when two horizontal bars with different gap in between them
(gh ) were placed on top and bottom of the tray carriers
148
Bibliography
Ajandouz, E., Tchiakpe, L., Dalle Ore, F., Benajiba, A. & Puigserver, A. (2001). Effects of pH
on caramelization and Maillard reaction kinetics in fructose-lysine Model systems. Food
chemistry, 66(7), 926–931.
Ames, W. F. (2014). Numerical methods for partial differential equations. Academic press.
Appert, N. (1812). The art of preserving all kinds of animal and vegetable substances for several
years: A work published by the order of the french minister of the interior, on the report of
the board of arts and manufacturers.
Ayappa, K. & Davis, H. (1991). Microwave heating: An evaluation of power formulations. Chemical Engineering Science, 46(4), 1005–1016.
Balanis, C. A. (2005). Antenna theory analysis and design (3rd ed.). New Jersey: John Wiley &
Sons, Inc.
Barringer, S., Davis, E., Gordon, J., Ayappa, K. & H.T, D. (1995). Microwave-heating temperature
profiles for thin slabs compared to Maxwell and Lambert law predictions. Journal of food
science, 60(5), 1137–1142.
Bathe, K.-J. & Wilson, E. L. (1976). Numerical methods in finite element analysis. Prentice-Hall
Englewood Cliffs, NJ.
Bengtsson, N. E. & Ohlsson, T. (1974). Microwave heating in the food industry. Proceedings of
the IEEE, 62(1), 44–55.
Bergman, T. L. & Incropera, F. P. (2011). Fundamentals of heat and mass transfer. John Wiley &
Sons.
Bornhorst, E. R., Tang, J., Sablani, S. S. & Barbosa Cánovas, G. V. (2017). Development of model
food systems for thermal pasteurization applications based on Maillard reaction products.
LWT-Food science and technology, 75, 417–424.
149
Campanone, L. & Zaritzky, N. (2005). Mathematical analysis of microwave heating process. Journal
of Food Engineering, 69(3), 359–368.
Celuch, M & Kopyt, P. (2009). Modeling microwave heating in foods. Development of Packaging
and Products for Use in Microwave Ovens, 305–348.
Chen, H., Tang, J. & Liu, F. (2008). Simulation model for moving food packages in microwave
heating processes using conformal FDTD method. Journal of Food Engineering, 88(3), 294–
305.
Chen, H., Tang, J. & Liu, F. (2007). Coupled simulation of an electromagnetic heating process
using the finite difference time domain method. Journal of Microwave Power and Electromagnetic Energy, 41(3), 50.
Chew, W. C., Michielssen, E., Song, J. & Jin, J.-M. (2001). Fast and efficient algorithms in computational electromagnetics. Artech House, Inc.
Datta, A. K. (1990). Heat and mass transfer in the microwave processing of food. Chemical Engineering Progress, 86(6), 47–53.
Dibben, D. (2001a). Electromagnetics : Fundamental aspects and numerical modeling. In A. Datta
& R. Anantheswaran (Eds.), Microwave technology for food applications (1st ed., pp. 1–28).
New York: Marcel Dekker, Inc.
Dibben, D. (2001b). Handbook of microwave technology for food applications (1st ed.) (A. Datta
& R. Anantheswaran, Eds.). New York: Marcel Dekker, Inc.
Eggleston, G. & Vercellotti, J. R. (2000). Degradation of sucrose, glucose and fructose in concentrated qqueous solutions under constant pH conditions at elevated temperature. Journal of
Carbohydrate Chemistry, 19(9), 1305–1318.
Farkas, D. F. (2003). Food engineering history. Encyclopedia of Agricultural Food and Biological
Engineering, New York: Marcel Dekker, 346–349.
150
Gehlhar, M. & Regmi, A. (2005). Factors shaping global food markets. New directions in global
food markets, 5–17.
Gentry, T. S. & Roberts, J. S. (2004). Formation kinetics and application of 5-hydroxymethylfurfural
as a time–temperature indicator of lethality for continuous pasteurization of apple cider. Innovative Food Science & Emerging Technologies, 5(3), 327–333.
Goedeken, D., Tong, C. & Virtanen, A. (1997). Dielectric properties of a pregelatinized bread
system at 2450 MHz as a function of temperature, moisture, salt and specific volume. Journal
of Food Science, 62(1), 145–149.
Guan, D, Cheng, M, Wang, Y & Tang, J. (2004). Dielectric properties of mashed potatoes relevant
to microwave and radio-frequency pasteurization and sterilization processes. Food Engineering and Physical Properties, 69(1).
Gupta, R., Mikhaylenko, G., Balasubramaniam, V. & Tang, J. (2011). Combined pressure–temperature
effects on the chemical marker (4-hydroxy-5-methyl-3 (2h)-furanone) formation in whey
protein gels. LWT-Food Science and Technology, 44(10), 2141–2146.
Harlfinger, L. (1992). Microwave sterilization. Food technology (USA).
Hendrickx, M. E., Weng, Z., Maesmans, G. & Tobback, P. (1992). Validation of a time-temperature
integrator for thermal processing of foods under pasteurization conditions. International
Journal of Food Science & Technology, 27, 21–31.
Holdsworth, S. (1997). Thermal processing of packaged foods (1st ed.). London: Chapman & Hall.
Hossan, M. & Dutta, P. (2012). Effects of temperature dependent properties in electromagnetic
heating. International Journal of Heat and Mass Transfer, 55(13), 3412–3422.
Jain, D., Wang, J., Liu, F., Tang, J. & Bohnet, S. (2017a). Application of non-enzymatic browning
of fructose for heating pattern determination in microwave assisted thermal pasteurization
system. Journal of Food Engineering, 210, 27–34.
151
Jain, D., Tang, J., Pedrow, P., Tang, Z. & Sablani, S. (2017b). Influence of dielectric properties and
thickness on electromagnetic heating of foods in 915 MHz single mode microwave cavity.
Journal of Food Engineering-under review.
Kim, H. B., Tadini, C. C. & Singh, R. K. (1999). Effect of different pasteurization conditions
on enzyme inactivation of orange juice in pilot-scale experiments. Journal of food process
engineering, 22(5), 395–403.
Kim, H.-J., Taub, I. A., Choi, Y.-M. & Anuradha, P. (1996). Principles and applications of chemical
markers of sterility in high temperature Short time processing of particulate foods. In T.-C.
Lee & H.-J. Kim (Eds.), Chemical markers for processed and stored foods (1st ed., Chap. 6,
pp. 54–69). Rutgers: American Chemical Society.
Komarov, V. V. & Tang, J. (2004). Dielectric permittivity and loss factor of tap water at 915 MHz.
Microwave and Optical Technology Letters, 42(5), 419–420.
Kunz, K. S. & Luebbers, R. J. (1993). The finite difference time domain method for electromagnetics. CRC press.
Labuza, T. P. & Baisier, W. M. (1992). The kinetics of non-enzymatic browning. In H. G. Schwartzberg
& R. W. Hartel (Eds.), Physical chemistry of foods (Chap. 14, pp. 595–649). New York: Marcel Dekker, Inc.
Latour, B. (1993). The pasteurization of france. Harvard University Press.
Lau, M., Tang, J., Taub, I., Yang, T., Edwards, C. & Mao, R. (2003a). Kinetics of chemical marker
formation in whey protein gels for studying high temperature short time microwave sterilization. Journal of Food Engineering, 60, 397–405.
Lau, M., Tang, J, Taub, I., Yang, T., Edwards, C. & Mao, R. (2003b). Kinetics of chemical marker
formation in whey protein gels for studying microwave sterilization. Journal of food Engineering, 60(4), 397–405.
152
Ledl, F., Schnell, W. & Severin, T. (1995). Nachweis von 2,3-dihydro-3,5-dihydroxy-6-methyl4H-pyran-4-on in lebensmitteln. Lebensmittel-Untersuchung und-Forschung, 51(17), 4947–
4952.
Luan, D., Tang, J., Pedrow, P. D., Liu, F. & Tang, Z. (2016). Analysis of electric field distribution
within a microwave assisted thermal sterilization (MATS) system by computer simulation.
Journal of Food Engineering, 188, 87–97.
Luan, D., Tang, J., Liu, F., Tang, Z., Li, F., Lin, H. & Stewart, B. (2015a). Dielectric properties
of bentonite water pastes used for stable loads in microwave thermal processing systems.
Journal of Food Engineering, 161, 40–47.
Luan, D., Wang, Y., Tang, J. & Jain, D. (2017). Frequency distribution in domestic microwave
ovens and its influence on heating pattern. Journal of food science, 82(2), 429–436.
Luan, D., Tang, J., Pedrow, P. D., Liu, F. & Tang, Z. (2015b). Performance of mobile metallic
temperature sensors in high power microwave heating systems. Journal of Food Engineering,
149, 114–122.
Luan, D., Tang, J., Pedrow, P. D., Liu, F. & Tang, Z. (2013). Using mobile metallic temperature
sensors in continuous microwave assisted sterilization (MATS) systems. Journal of Food
Engineering, 119(3), 552–560.
Martins, S. I., Jongen, W. M. & Boekel, M. A. V. (2000). A review of Maillard reaction in food and
implications to kinetic modelling. Trends in Food Science & Technology, 11(9-10), 364–373.
Morris, C. (1996). Manufacturing forecast accelerating changes. Food Eng, 73–7.
Nelson, S. & Datta, A. (2001). Dielectric properties of food materials and electric field interactions.
In A. Datta & R. Anantheswaran (Eds.), Microwave technology for food applications (1st ed.,
pp. 69–107). New York: Marcel Dekker, Inc.
153
Nott, K. P. & Hall, L. D. (1999). Advances in temperature validation of foods. Trends in Food
Science & Technology, 10(11), 366–374.
Oliveira, M. & Franca, A. (2002). Microwave heating of foodstuffs. Journal of Food engineering,
53(4), 347–359.
Pandit, R., Tang, J., Liu, F. & Mikhaylenko, G. (2007a). A computer vision method to locate cold
spots in foods in microwave sterilization processes. Pattern Recognition, 40(12), 3667–3676.
Pandit, R., Tang, J., Liu, F. & Mikhaylenko, G. (2007b). A computer vision method to locate cold
spots in foods in microwave sterilization processes. The journal of the pattern recognition
society, 46(12), 3667–3676.
Pandit, R., Tang, J., Mikhaylenko, G. & Liu, F. (2006). Kinetics of chemical marker M-2 formation
in mashed potato - a tool to locate cold spots under microwave sterilization. Journal of Food
Engineering, 76(3), 353–361.
Pathak, S., Liu, F & Tang, J. (2003). Finite difference time domain (FDTD) characterization of
a single mode applicator. Journal of Microwave Power and Electromagnetic Energy, 38(1),
37–48.
Peng, J., Tang, J., Jiao, Y., Bohnet, S. G. & Barrett, D. M. (2013). Dielectric properties of tomatoes
assisting in the development of microwave pasteurization and sterilization processes. LWTFood Science and Technology, 54(2), 367–376.
Peng, J., Tang, J., Barrett, D. M., Sablani, S. S. & Powers, J. R. (2014). Kinetics of carrot texture
degradation under pasteurization conditions. Journal of Food Engineering, 122(1), 84–91.
Peng, J., Tang, J., Luan, D., Liu, F., Tang, Z., Li, F. & Zhang, W. (2017a). Microwave pasteurization
of pre-packaged carrots. Journal of Food Engineering, 202, 56–64.
154
Peng, J., Tang, J., Barrett, D. M., Sablani, S. S., Anderson, N. & Powers, J. R. (2017b). Thermal
pasteurization of ready-to-eat foods and vegetables: Critical factors for process design and
effects on quality. Critical reviews in food science and nutrition, 57(14), 2970–2995.
Pitchai, K. (2011). Electromagnetic and heat transfer modeling of microwave heating in domestic
ovens (Doctoral dissertation, University of Nebraska at Lincoln).
Prescott, S. & Underwood, W. L. (1897). Contributions to our knowledge of micro-organisms and
sterilizing processes in the canning industries. Science, 6(152), 800–802.
Ramaswamy, H., Awuah, G., Kim, H.-J. & Choi, Y.-M. (1996). Evaluation of a chemical marker
for process lethality measurement at 110°C in a continuous flow holding tube. Journal of
Food processing and preservation, 20, 235–249.
Remmen Henk, H., Ponne, C., Nijhuis, H., Bartels, P. & Kerkhof, P. J. (1996). Microwave heating
distributions in slabs, spheres and cylinders with relation to food processing. Journal of food
science, 61(6), 1105–1114.
Resurreccion, F. P. (2012). Microwave assisted thermal processing of homogeneous and heterogeneous food packed in a polymeric container (Doctoral dissertation, Washington State University).
Resurreccion, F. P., Luan, D, Tang, J, Liu, F, Tang, Z, Pedrow, P. D. & Cavalieri, R. (2015a). Effect
of changes in microwave frequency on heating patterns of foods in a microwave assisted
thermal sterilization system. Journal of Food Composition and Analysis, 150, 99–105.
Resurreccion, F., Tang, J., Pedrow, P., Cavalieri, R., Liu, F. & Tang, Z. (2013). Development of a
computer simulation model for processing food in a microwave assisted thermal sterilization
(MATS) system. Journal of Food Engineering, 118(4), 406–416.
155
Resurreccion, F., Luan, D, Tang, J, Liu, F, Tang, Z, Pedrow, P. & Cavalieri, R. (2015b). Effect
of changes in microwave frequency on heating patterns of foods in a microwave assisted
thermal sterilization system. Journal of Food Engineering, 150, 99–105.
Risman, P. O. & Celuch-Marcysiak, M. (2000). Electromagnetic modelling for microwave heating
applications. In Microwaves, radar and wireless communications. 2000. mikon-2000. 13th
international conference on (Vol. 3, pp. 167–182). IEEE.
Ross, E. W. (1993). Relation of bacterial destruction to chemical marker formation during processing by thermal pulses. Journal of Food Process Engineering, 16, 247–270.
Sablani, S. S., Bruno, L., Kasapis, S. & Symaladevi, R. M. (2009). Thermal transitions of rice:
Development of a state diagram. Journal of Food Engineering, 90(1), 110–118.
Sadiku, N. M. (2010). Elements of Electromagnetics (5th). Oxford University Press.
Shaw, P. E., Tatum, J. H. & Berry, R. E. (1968). Base-catalysed fructose degradation and its relation
to nonenzymatic browning. Journal of Agricultural and Food Chemistry, 16(6), 979–982.
Shaw, P. E., Tatum, J. H. & Berry, R. E. (1971). 2, 3-dihydro-3, 5-dihydroxy-6-methyl-4h-pyran4-one, a degradation product of a hexose. Carbohydrate Research, 16(1), 207–211.
Sipahioglu, O & Barringer, S. (2003). Dielectric properties of vegetables and fruits as a function
of temperature, ash, and moisture content. Journal of food science, 68(1), 234–239.
Sipahioglu, O., Barringer, S. A., Taub, I. & Prakash, A. (2003). Modeling the dielectric properties
of ham as a function of temperature and composition. Journal of Food Science, 68(3), 904–
909.
Smith, L. et al. (1977). Botulism. the organism, its toxins, the disease. Charles C. Thomas, 301-327
East Lawrence Avenue Springfield, Illinois 62717, USA.
Stumbo, C. R. (1973). Thermobacteriology in food processing. Academic Press, New York.
Sun, D. (2014). Emerging technologies for food processing. Elsevier, Oxford.
156
Taflove, A. & Hagness C., S. (1995). Computation Electrodynamics- The Finite- Difference TimeDomain Method (2nd ed.). Boston: Artech House.
Tang, J, Tung, M. & Zeng, Y. (1997). Gelling properties of gellan solutions containing monovalent
and divalent cations. Journal of Food Science, 62(4), 688–712.
Tang, J. (2015). Unlocking Potentials of Microwaves for Food Safety and Quality. Journal of Food
Science, 80(8), E1776–E1793.
Tang, J. & Liu, F. (2017). Microwave sterilization or pasteurization. US Patent 9,642,385. Google
Patents.
Tang, J. & Resurreccion, F. P. (2009). Electromagnetic basis of microwave heating. In M. W.
Lorence & P. S. Pescheck (Eds.), Development of packaging and products for use in microwave ovens (1st ed., pp. 3–36). Boca Raton, Florida: CRC press.
Tang, J., Liu, F., Pathak, S. K. & Eugene, E. E. I. (2006). Apparatus and method for heating objects
with microwaves. US Patent 7,119,313. Google Patents.
Tang, J., Tung, M. A. & Zeng, Y. (1996). Compression strength and deformation of gellan gels
formed with mono-and divalent cations. Carbohydrate polymers, 29(1), 11–16.
Tang, J., Lelievre, J., Tung, M. A. & Zeng, Y. (1994). Polymer and ion concentration effects on
gellan gel strength and strain. Journal of Food Science, 59(1), 216–220.
Tang, Z., Mikhaylenko, G., Liu, F., Mah, J.-H., Pandit, R., Younce, F. & Tang, J. (2008). Microwave
sterilization of sliced beef in gravy in 7-oz trays. Journal of Food Engineering, 89(4), 375–
383.
Wang, R., Zhang, M., Mujumdar, A. S. & Jiang, H. (2011). Effect of salt and sucrose content on
dielectric properties and microwave freeze drying behavior of re-structured potato slices.
Journal of Food Engineering, 106(4), 290–297.
157
Wang, Y., Lau, M. H., Tang, J. & Mao, R. (2004). Kinetics of chemical marker M-1 formation in
whey protein gels for developing sterilization processes based on dielectric heating. Journal
of Food Engineering, 64(1), 111–118.
Wang, Y., Wig, T. D., Tang, J. & Hallberg, L. M. (2003). Dielectric properties of foods relevant to
RF and microwave pasteurization and sterilization. Journal of Food Engineering, 57, 257–
268.
Wang, Y., Tang, J., Rasco, B., Kong, F. & Wang, S. (2008). Dielectric properties of salmon fillets as
a function of temperature and composition. Journal of Food Engineering, 87(2), 236 –246.
Wnorowski, A & Yaylayan, V. (2002). Prediction of process lethality through measurement of
maillard-generated chemical markers. Journal of food science, 67(6), 2149–2152.
Yang, H. & Gunasekaran, S. (2004). Comparison of temperature distribution in model food cylinders based on Maxwell’s equations and Lambert’s law during pulsed microwave heating.
Journal of Food Engineering, 64(4), 445–453.
Zhang, H. & Datta, A. (2001). Electromagnetics of microwave heating: magnitude and uniformity of energy absorption in an oven. In A. Datta & R. Anantheswaran (Eds.), Microwave
technology for food applications (1st ed., pp. 33–63). New York: Marcel Dekker, Inc.
Zhang, L., Lyng, J. G. & Brunton, N. P. (2007). The effect of fat, water and salt on the thermal
and dielectric properties of meat batter and its temperature following microwave or radio
frequency heating. Journal of Food Engineering, 80(1), 142–151.
Zhang, W., Tang, J., Liu, F., Bohnet, S. & Tang, Z. (2014). Chemical marker M2 (4-hydroxy-5methyl-3(2H)-furanone) formation in egg white gel model for heating pattern determination
of microwave-assisted pasteurization processing. Journal of Food Engineering, 125, 69–76.
158
Zhang, W., Luan, D., Tang, J., Sablani, S. S., Rasco, B., Lin, H. & Liu, F. (2015). Dielectric
properties and other physical properties of low-acyl gellan gel as relevant to microwave
assisted pasteurization process. Journal of Food Engineering, 149, 195–203.
159
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